LMFDB - Embedded newform 546.2.bx.b.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.6
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.b.349.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.46294 - 2.46294i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.0731721 + 2.64474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.46294 - 2.46294i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.0731721 + 2.64474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.74156 - 3.01647i) q^{10} +(-5.73180 + 1.53583i) q^{11} -1.00000 q^{12} +(-2.00189 + 2.99874i) q^{13} +(-2.53568 + 0.755188i) q^{14} +(-0.901498 - 3.36444i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.681755 - 1.18083i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(0.203136 - 0.758114i) q^{19} +(3.36444 + 0.901498i) q^{20} +(-1.25900 + 2.32700i) q^{21} +(-2.96700 - 5.13899i) q^{22} +(-0.338051 - 0.195174i) q^{23} +(-0.258819 - 0.965926i) q^{24} +7.13213i q^{25} +(-3.41469 - 1.15755i) q^{26} +1.00000i q^{27} +(-1.38574 - 2.25383i) q^{28} +(-3.44143 + 5.96073i) q^{29} +(3.01647 - 1.74156i) q^{30} +(0.211182 + 0.211182i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-5.73180 - 1.53583i) q^{33} +(0.964147 - 0.964147i) q^{34} +(6.33361 - 6.69405i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-5.84975 + 1.56744i) q^{37} +0.784857 q^{38} +(-3.23306 + 1.59604i) q^{39} +3.48312i q^{40} +(-3.49404 + 0.936225i) q^{41} +(-2.57356 - 0.613830i) q^{42} +(2.10364 - 1.21454i) q^{43} +(4.19597 - 4.19597i) q^{44} +(0.901498 - 3.36444i) q^{45} +(0.101029 - 0.377047i) q^{46} +(6.84615 - 6.84615i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.98929 + 0.387042i) q^{49} +(-6.88911 + 1.84593i) q^{50} -1.36351i q^{51} +(0.234317 - 3.59793i) q^{52} +9.73688 q^{53} +(-0.965926 + 0.258819i) q^{54} +(17.8997 + 10.3344i) q^{55} +(1.81837 - 1.92185i) q^{56} +(0.554978 - 0.554978i) q^{57} +(-6.64833 - 1.78141i) q^{58} +(-5.37683 - 1.44072i) q^{59} +(2.46294 + 2.46294i) q^{60} +(8.38542 - 4.84132i) q^{61} +(-0.149328 + 0.258644i) q^{62} +(-2.25383 + 1.38574i) q^{63} +1.00000i q^{64} +(12.3162 - 2.45518i) q^{65} -5.93400i q^{66} +(1.38874 + 5.18284i) q^{67} +(1.18083 + 0.681755i) q^{68} +(-0.195174 - 0.338051i) q^{69} +(8.10521 + 4.38525i) q^{70} +(12.8877 + 3.45324i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-5.09775 + 5.09775i) q^{73} +(-3.02805 - 5.24474i) q^{74} +(-3.56607 + 6.17661i) q^{75} +(0.203136 + 0.758114i) q^{76} +(-4.48128 - 15.0467i) q^{77} +(-2.37843 - 2.70981i) q^{78} +9.25714 q^{79} +(-3.36444 + 0.901498i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.80865 - 3.13267i) q^{82} +(-9.33819 - 9.33819i) q^{83} +(-0.0731721 - 2.64474i) q^{84} +(-1.22920 + 4.58744i) q^{85} +(1.71762 + 1.71762i) q^{86} +(-5.96073 + 3.44143i) q^{87} +(5.13899 + 2.96700i) q^{88} +(-1.44141 - 5.37940i) q^{89} +3.48312 q^{90} +(-8.07737 - 5.07505i) q^{91} +0.390347 q^{92} +(0.0772979 + 0.288480i) q^{93} +(8.38479 + 4.84096i) q^{94} +(-2.36750 + 1.36688i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-3.44763 + 12.8667i) q^{97} +(-2.18282 - 6.65096i) q^{98} +(-4.19597 - 4.19597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.46294	−	2.46294i	−1.10146	−	1.10146i	−0.994235	−	0.107225i	$-0.965804\pi$
$5$	−2.46294	−	2.46294i	−1.10146	−	1.10146i	−0.107225	−	0.994235i	$-0.534196\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	0.0731721	+	2.64474i	0.0276565	+	0.999617i
$7$	0.0731721	+	2.64474i	0.0276565	+	0.999617i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.74156	−	3.01647i	0.550730	−	0.953892i
$11$	−5.73180	+	1.53583i	−1.72820	+	0.463071i	−0.979768	−	0.200137i	$-0.935861\pi$
$11$	−5.73180	+	1.53583i	−1.72820	+	0.463071i	−0.748435	+	0.663208i	$0.769194\pi$
$12$	−1.00000			−0.288675
$13$	−2.00189	+	2.99874i	−0.555224	+	0.831701i
$13$	−2.00189	+	2.99874i	−0.555224	+	0.831701i
$14$	−2.53568	+	0.755188i	−0.677690	+	0.201832i
$15$	−0.901498	−	3.36444i	−0.232766	−	0.868694i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.681755	−	1.18083i	−0.165350	−	0.286394i	0.771430	−	0.636315i	$-0.219542\pi$
$17$	−0.681755	−	1.18083i	−0.165350	−	0.286394i	−0.936779	+	0.349920i	$0.886209\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	0.203136	−	0.758114i	0.0466026	−	0.173923i	−0.938702	−	0.344730i	$-0.887971\pi$
$19$	0.203136	−	0.758114i	0.0466026	−	0.173923i	0.985305	+	0.170806i	$0.0546373\pi$
$20$	3.36444	+	0.901498i	0.752311	+	0.201581i
$21$	−1.25900	+	2.32700i	−0.274736	+	0.507792i
$22$	−2.96700	−	5.13899i	−0.632566	−	1.09564i
$23$	−0.338051	−	0.195174i	−0.0704884	−	0.0406965i	0.464342	−	0.885656i	$-0.346291\pi$
$23$	−0.338051	−	0.195174i	−0.0704884	−	0.0406965i	−0.534830	+	0.844960i	$0.679624\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$			7.13213i			1.42643i
$26$	−3.41469	−	1.15755i	−0.669675	−	0.227013i
$27$			1.00000i			0.192450i
$28$	−1.38574	−	2.25383i	−0.261880	−	0.425933i
$29$	−3.44143	+	5.96073i	−0.639057	+	1.10688i	0.346583	+	0.938019i	$0.387342\pi$
$29$	−3.44143	+	5.96073i	−0.639057	+	1.10688i	−0.985640	+	0.168860i	$0.945991\pi$
$30$	3.01647	−	1.74156i	0.550730	−	0.317964i
$31$	0.211182	+	0.211182i	0.0379294	+	0.0379294i	0.725817	−	0.687888i	$-0.241462\pi$
$31$	0.211182	+	0.211182i	0.0379294	+	0.0379294i	−0.687888	+	0.725817i	$0.741462\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−5.73180	−	1.53583i	−0.997778	−	0.267354i
$34$	0.964147	−	0.964147i	0.165350	−	0.165350i
$35$	6.33361	−	6.69405i	1.07058	−	1.13150i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−5.84975	+	1.56744i	−0.961693	+	0.257685i	−0.705317	−	0.708892i	$-0.749195\pi$
$37$	−5.84975	+	1.56744i	−0.961693	+	0.257685i	−0.256376	+	0.966577i	$0.582528\pi$
$38$	0.784857			0.127321
$39$	−3.23306	+	1.59604i	−0.517703	+	0.255571i
$40$			3.48312i			0.550730i
$41$	−3.49404	+	0.936225i	−0.545677	+	0.146214i	−0.521118	−	0.853485i	$-0.674485\pi$
$41$	−3.49404	+	0.936225i	−0.545677	+	0.146214i	−0.0245592	+	0.999698i	$0.507818\pi$
$42$	−2.57356	−	0.613830i	−0.397109	−	0.0947160i
$43$	2.10364	−	1.21454i	0.320803	−	0.185216i	−0.330948	−	0.943649i	$-0.607368\pi$
$43$	2.10364	−	1.21454i	0.320803	−	0.185216i	0.651750	+	0.758434i	$0.274035\pi$
$44$	4.19597	−	4.19597i	0.632566	−	0.632566i
$45$	0.901498	−	3.36444i	0.134387	−	0.501541i
$46$	0.101029	−	0.377047i	0.0148960	−	0.0555925i
$47$	6.84615	−	6.84615i	0.998614	−	0.998614i	−0.00138548	−	0.999999i	$-0.500441\pi$
$47$	6.84615	−	6.84615i	0.998614	−	0.998614i	0.999999	+	0.00138548i	$0.000441014\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−6.98929	+	0.387042i	−0.998470	+	0.0552918i
$50$	−6.88911	+	1.84593i	−0.974267	+	0.261054i
$51$		−	1.36351i		−	0.190930i
$52$	0.234317	−	3.59793i	0.0324940	−	0.498943i
$53$	9.73688			1.33746			0.668732	−	0.743504i	$-0.266837\pi$
$53$	9.73688			1.33746			0.668732	+	0.743504i	$0.266837\pi$
$54$	−0.965926	+	0.258819i	−0.131446	+	0.0352208i
$55$	17.8997	+	10.3344i	2.41360	+	1.39349i
$56$	1.81837	−	1.92185i	0.242990	−	0.256818i
$57$	0.554978	−	0.554978i	0.0735086	−	0.0735086i
$58$	−6.64833	−	1.78141i	−0.872969	−	0.233911i
$59$	−5.37683	−	1.44072i	−0.700004	−	0.187566i	−0.108772	−	0.994067i	$-0.534692\pi$
$59$	−5.37683	−	1.44072i	−0.700004	−	0.187566i	−0.591232	+	0.806501i	$0.701358\pi$
$60$	2.46294	+	2.46294i	0.317964	+	0.317964i
$61$	8.38542	−	4.84132i	1.07364	−	0.619868i	0.144468	−	0.989509i	$-0.453853\pi$
$61$	8.38542	−	4.84132i	1.07364	−	0.619868i	0.929174	+	0.369642i	$0.120520\pi$
$62$	−0.149328	+	0.258644i	−0.0189647	+	0.0328478i
$63$	−2.25383	+	1.38574i	−0.283955	+	0.174587i
$64$			1.00000i			0.125000i
$65$	12.3162	−	2.45518i	1.52764	−	0.304528i
$66$		−	5.93400i		−	0.730425i
$67$	1.38874	+	5.18284i	0.169661	+	0.633185i	0.997400	+	0.0720702i	$0.0229606\pi$
$67$	1.38874	+	5.18284i	0.169661	+	0.633185i	−0.827738	+	0.561114i	$0.810373\pi$
$68$	1.18083	+	0.681755i	0.143197	+	0.0826749i
$69$	−0.195174	−	0.338051i	−0.0234961	−	0.0406965i
$70$	8.10521	+	4.38525i	0.968758	+	0.524138i
$71$	12.8877	+	3.45324i	1.52948	+	0.409824i	0.922850	−	0.385158i	$-0.125853\pi$
$71$	12.8877	+	3.45324i	1.52948	+	0.409824i	0.606633	+	0.794982i	$0.292520\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−5.09775	+	5.09775i	−0.596647	+	0.596647i	−0.939419	−	0.342772i	$-0.888634\pi$
$73$	−5.09775	+	5.09775i	−0.596647	+	0.596647i	0.342772	+	0.939419i	$0.388634\pi$
$74$	−3.02805	−	5.24474i	−0.352004	−	0.609689i
$75$	−3.56607	+	6.17661i	−0.411774	+	0.713213i
$76$	0.203136	+	0.758114i	0.0233013	+	0.0869616i
$77$	−4.48128	−	15.0467i	−0.510689	−	1.71474i
$78$	−2.37843	−	2.70981i	−0.269304	−	0.306825i
$79$	9.25714			1.04151			0.520755	−	0.853706i	$-0.325651\pi$
$79$	9.25714			1.04151			0.520755	+	0.853706i	$0.325651\pi$
$80$	−3.36444	+	0.901498i	−0.376155	+	0.100791i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.80865	−	3.13267i	−0.199732	−	0.345946i
$83$	−9.33819	−	9.33819i	−1.02500	−	1.02500i	−0.999679	−	0.0253199i	$-0.991940\pi$
$83$	−9.33819	−	9.33819i	−1.02500	−	1.02500i	−0.0253199	−	0.999679i	$-0.508060\pi$
$84$	−0.0731721	−	2.64474i	−0.00798373	−	0.288565i
$85$	−1.22920	+	4.58744i	−0.133326	+	0.497578i
$86$	1.71762	+	1.71762i	0.185216	+	0.185216i
$87$	−5.96073	+	3.44143i	−0.639057	+	0.368960i
$88$	5.13899	+	2.96700i	0.547818	+	0.316283i
$89$	−1.44141	−	5.37940i	−0.152789	−	0.570215i	−0.999285	−	0.0378199i	$-0.987959\pi$
$89$	−1.44141	−	5.37940i	−0.152789	−	0.570215i	0.846496	−	0.532395i	$-0.178708\pi$
$90$	3.48312			0.367153
$91$	−8.07737	−	5.07505i	−0.846738	−	0.532010i
$92$	0.390347			0.0406965
$93$	0.0772979	+	0.288480i	0.00801542	+	0.0299139i
$94$	8.38479	+	4.84096i	0.864825	+	0.499307i
$95$	−2.36750	+	1.36688i	−0.242900	+	0.140239i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−3.44763	+	12.8667i	−0.350054	+	1.30642i	0.536541	+	0.843874i	$0.319731\pi$
$97$	−3.44763	+	12.8667i	−0.350054	+	1.30642i	−0.886595	+	0.462546i	$0.846936\pi$
$98$	−2.18282	−	6.65096i	−0.220498	−	0.671849i
$99$	−4.19597	−	4.19597i	−0.421711	−	0.421711i
$100$	−3.56607	−	6.17661i	−0.356607	−	0.617661i
$101$	−8.86523	+	15.3550i	−0.882123	+	1.52788i	−0.0331469	+	0.999450i	$0.510553\pi$
$101$	−8.86523	+	15.3550i	−0.882123	+	1.52788i	−0.848976	+	0.528431i	$0.822780\pi$
$102$	1.31705	−	0.352902i	0.130407	−	0.0349425i
$103$	2.94833			0.290508			0.145254	−	0.989394i	$-0.453600\pi$
$103$	2.94833			0.290508			0.145254	+	0.989394i	$0.453600\pi$
$104$	3.53598	−	0.704879i	0.346731	−	0.0691191i
$105$	8.83209	−	2.63041i	0.861924	−	0.256702i
$106$	2.52009	+	9.40511i	0.244773	+	0.913505i
$107$	−1.37037	+	2.37355i	−0.132479	+	0.229460i	−0.924631	−	0.380863i	$-0.875627\pi$
$107$	−1.37037	+	2.37355i	−0.132479	+	0.229460i	0.792153	+	0.610323i	$0.208960\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.77402	+	5.77402i	−0.553051	+	0.553051i	−0.927320	−	0.374269i	$-0.877894\pi$
$109$	−5.77402	+	5.77402i	−0.553051	+	0.553051i	0.374269	+	0.927320i	$0.377894\pi$
$110$	−5.34949	+	19.9646i	−0.510054	+	1.90355i
$111$	−5.84975	−	1.56744i	−0.555233	−	0.148774i
$112$	2.32700	+	1.25900i	0.219881	+	0.118964i
$113$	3.17554	+	5.50020i	0.298730	+	0.517415i	0.975846	−	0.218461i	$-0.0701037\pi$
$113$	3.17554	+	5.50020i	0.298730	+	0.517415i	−0.677116	+	0.735876i	$0.736770\pi$
$114$	0.679706	+	0.392429i	0.0636603	+	0.0367543i
$115$	0.351897	+	1.31330i	0.0328146	+	0.122466i
$116$		−	6.88286i		−	0.639057i
$117$	−3.59793	−	0.234317i	−0.332629	−	0.0216626i
$118$		−	5.56651i		−	0.512439i
$119$	3.07311	−	1.88947i	0.281712	−	0.173207i
$120$	−1.74156	+	3.01647i	−0.158982	+	0.275365i
$121$	20.9685	−	12.1062i	1.90623	−	1.10056i
$122$	6.84666	+	6.84666i	0.619868	+	0.619868i
$123$	−3.49404	−	0.936225i	−0.315047	−	0.0844166i
$124$	−0.288480	−	0.0772979i	−0.0259062	−	0.00694155i
$125$	5.25131	−	5.25131i	0.469692	−	0.469692i
$126$	−1.92185	−	1.81837i	−0.171212	−	0.161994i
$127$	−11.2797	−	6.51235i	−1.00091	−	0.577877i	−0.0923947	−	0.995722i	$-0.529452\pi$
$127$	−11.2797	−	6.51235i	−1.00091	−	0.577877i	−0.908518	+	0.417845i	$0.862785\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	2.42908			0.213868
$130$	5.55920	+	11.2611i	0.487574	+	0.987666i
$131$			22.5136i			1.96702i	0.180841	+	0.983512i	$0.442118\pi$
$131$			22.5136i			1.96702i	−0.180841	+	0.983512i	$0.557882\pi$
$132$	5.73180	−	1.53583i	0.498889	−	0.133677i
$133$	2.01988	+	0.481769i	0.175146	+	0.0417747i
$134$	−4.64681	+	2.68284i	−0.401423	+	0.231762i
$135$	2.46294	−	2.46294i	0.211976	−	0.211976i
$136$	−0.352902	+	1.31705i	−0.0302611	+	0.112936i
$137$	−5.53036	+	20.6396i	−0.472491	+	1.76336i	0.158283	+	0.987394i	$0.449404\pi$
$137$	−5.53036	+	20.6396i	−0.472491	+	1.76336i	−0.630774	+	0.775966i	$0.717263\pi$
$138$	0.276017	−	0.276017i	0.0234961	−	0.0234961i
$139$	−13.2381	+	7.64304i	−1.12284	+	0.648274i	−0.942125	−	0.335261i	$-0.891176\pi$
$139$	−13.2381	+	7.64304i	−1.12284	+	0.648274i	−0.180718	+	0.983535i	$0.557842\pi$
$140$	−2.13804	+	8.96402i	−0.180698	+	0.757598i
$141$	9.35201	−	2.50586i	0.787582	−	0.211032i
$142$			13.3423i			1.11966i
$143$	6.86887	−	20.2627i	0.574404	−	1.69446i
$144$	1.00000			0.0833333
$145$	23.1569	−	6.20488i	1.92308	−	0.515288i
$146$	−6.24345	−	3.60466i	−0.516711	−	0.298323i
$147$	−6.24643	−	3.15946i	−0.515196	−	0.260588i
$148$	4.28231	−	4.28231i	0.352004	−	0.352004i
$149$	1.20776	+	0.323617i	0.0989433	+	0.0265118i	0.307951	−	0.951402i	$-0.400357\pi$
$149$	1.20776	+	0.323617i	0.0989433	+	0.0265118i	−0.209008	+	0.977914i	$0.567023\pi$
$150$	−6.88911	−	1.84593i	−0.562494	−	0.150720i
$151$	10.7007	+	10.7007i	0.870812	+	0.870812i	0.992561	−	0.121749i	$-0.0388504\pi$
$151$	10.7007	+	10.7007i	0.870812	+	0.870812i	−0.121749	+	0.992561i	$0.538850\pi$
$152$	−0.679706	+	0.392429i	−0.0551315	+	0.0318302i
$153$	0.681755	−	1.18083i	0.0551166	−	0.0954648i
$154$	13.3742	−	8.22297i	1.07772	−	0.662626i
$155$		−	1.04026i		−	0.0835553i
$156$	2.00189	−	2.99874i	0.160279	−	0.240091i
$157$		−	14.5407i		−	1.16048i	−0.814447	−	0.580238i	$-0.802959\pi$
$157$		−	14.5407i		−	1.16048i	0.814447	−	0.580238i	$-0.197041\pi$
$158$	2.39592	+	8.94171i	0.190609	+	0.711364i
$159$	8.43239	+	4.86844i	0.668732	+	0.386093i
$160$	−1.74156	−	3.01647i	−0.137682	−	0.238473i
$161$	0.491447	−	0.908337i	0.0387315	−	0.0715870i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	4.75964	−	17.7632i	0.372804	−	1.39132i	−0.483723	−	0.875221i	$-0.660716\pi$
$163$	4.75964	−	17.7632i	0.372804	−	1.39132i	0.856527	−	0.516102i	$-0.172617\pi$
$164$	2.55781	−	2.55781i	0.199732	−	0.199732i
$165$	10.3344	+	17.8997i	0.804533	+	1.39349i
$166$	6.60310	−	11.4369i	0.512500	−	0.887675i
$167$	−5.97631	−	22.3039i	−0.462460	−	1.72593i	−0.665174	−	0.746688i	$-0.731643\pi$
$167$	−5.97631	−	22.3039i	−0.462460	−	1.72593i	0.202714	−	0.979238i	$-0.435024\pi$
$168$	2.53568	−	0.755188i	0.195632	−	0.0582640i
$169$	−4.98488	−	12.0063i	−0.383452	−	0.923561i
$170$	−4.74927			−0.364252
$171$	0.758114	−	0.203136i	0.0579744	−	0.0155342i
$172$	−1.21454	+	2.10364i	−0.0926078	+	0.160401i
$173$	−3.62516	−	6.27896i	−0.275616	−	0.477380i	0.694675	−	0.719324i	$-0.255548\pi$
$173$	−3.62516	−	6.27896i	−0.275616	−	0.477380i	−0.970290	+	0.241944i	$0.922215\pi$
$174$	−4.86692	−	4.86692i	−0.368960	−	0.368960i
$175$	−18.8626	+	0.521873i	−1.42588	+	0.0394499i
$176$	−1.53583	+	5.73180i	−0.115768	+	0.432051i
$177$	−3.93612	−	3.93612i	−0.295857	−	0.295857i
$178$	4.82304	−	2.78458i	0.361502	−	0.208713i
$179$	−13.0221	−	7.51831i	−0.973317	−	0.561945i	−0.0730713	−	0.997327i	$-0.523280\pi$
$179$	−13.0221	−	7.51831i	−0.973317	−	0.561945i	−0.900246	+	0.435382i	$0.856613\pi$
$180$	0.901498	+	3.36444i	0.0671937	+	0.250770i
$181$	7.96888			0.592322			0.296161	−	0.955138i	$-0.404293\pi$
$181$	7.96888			0.592322			0.296161	+	0.955138i	$0.404293\pi$
$182$	2.81155	−	9.11566i	0.208406	−	0.675697i
$183$	9.68265			0.715762
$184$	0.101029	+	0.377047i	0.00744798	+	0.0277962i
$185$	18.2681	+	10.5471i	1.34309	+	0.775436i
$186$	−0.258644	+	0.149328i	−0.0189647	+	0.0109493i
$187$	5.72125	+	5.72125i	0.418379	+	0.418379i
$188$	−2.50586	+	9.35201i	−0.182759	+	0.682066i
$189$	−2.64474	+	0.0731721i	−0.192376	+	0.00532249i
$190$	−1.93306	−	1.93306i	−0.140239	−	0.140239i
$191$	−4.43523	−	7.68204i	−0.320922	−	0.555853i	0.659757	−	0.751479i	$-0.270659\pi$
$191$	−4.43523	−	7.68204i	−0.320922	−	0.555853i	−0.980679	+	0.195626i	$0.937326\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	3.54651	−	0.950284i	0.255283	−	0.0684030i	−0.128908	−	0.991657i	$-0.541147\pi$
$193$	3.54651	−	0.950284i	0.255283	−	0.0684030i	0.384191	+	0.923254i	$0.374480\pi$
$194$	−13.3206			−0.956366
$195$	11.8938	+	4.03187i	0.851730	+	0.288728i
$196$	5.85938	−	3.82983i	0.418527	−	0.273560i
$197$	3.90018	+	14.5557i	0.277877	+	1.03705i	0.953889	+	0.300159i	$0.0970398\pi$
$197$	3.90018	+	14.5557i	0.277877	+	1.03705i	−0.676013	+	0.736890i	$0.736294\pi$
$198$	2.96700	−	5.13899i	0.210855	−	0.365212i
$199$	4.30556	+	7.45745i	0.305213	+	0.528645i	0.977309	−	0.211820i	$-0.0679389\pi$
$199$	4.30556	+	7.45745i	0.305213	+	0.528645i	−0.672095	+	0.740464i	$0.734606\pi$
$200$	5.04318	−	5.04318i	0.356607	−	0.356607i
$201$	−1.38874	+	5.18284i	−0.0979540	+	0.365569i
$202$	−17.1263	−	4.58898i	−1.20500	−	0.322879i
$203$	−16.0164	−	8.66552i	−1.12413	−	0.608201i
$204$	0.681755	+	1.18083i	0.0477324	+	0.0826749i
$205$	10.9115	+	6.29974i	0.762090	+	0.439993i
$206$	0.763084	+	2.84787i	0.0531666	+	0.198420i
$207$		−	0.390347i		−	0.0271310i
$208$	1.59604	+	3.23306i	0.110665	+	0.224172i
$209$			4.65734i			0.322155i
$210$	4.82670	+	7.85035i	0.333074	+	0.541725i
$211$	−2.46370	+	4.26725i	−0.169608	+	0.293769i	−0.938282	−	0.345871i	$-0.887583\pi$
$211$	−2.46370	+	4.26725i	−0.169608	+	0.293769i	0.768674	+	0.639641i	$0.220917\pi$
$212$	−8.43239	+	4.86844i	−0.579139	+	0.334366i
$213$	9.43442	+	9.43442i	0.646436	+	0.646436i
$214$	−2.64735	−	0.709356i	−0.180969	−	0.0484905i
$215$	−8.17248	−	2.18981i	−0.557359	−	0.149344i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−0.543068	+	0.573973i	−0.0368659	+	0.0389638i
$218$	−7.07171	−	4.08285i	−0.478956	−	0.276526i
$219$	−6.96366	+	1.86591i	−0.470560	+	0.126086i
$220$	−20.6688			−1.39349
$221$	4.90581	+	0.319494i	0.330001	+	0.0214915i
$222$		−	6.05610i		−	0.406459i
$223$	−11.3141	+	3.03159i	−0.757646	+	0.203011i	−0.616907	−	0.787036i	$-0.711614\pi$
$223$	−11.3141	+	3.03159i	−0.757646	+	0.203011i	−0.140739	+	0.990047i	$0.544948\pi$
$224$	−0.613830	+	2.57356i	−0.0410132	+	0.171953i
$225$	−6.17661	+	3.56607i	−0.411774	+	0.237738i
$226$	−4.49089	+	4.49089i	−0.298730	+	0.298730i
$227$	−1.79513	+	6.69952i	−0.119147	+	0.444662i	−0.999564	−	0.0295384i	$-0.990596\pi$
$227$	−1.79513	+	6.69952i	−0.119147	+	0.444662i	0.880417	+	0.474201i	$0.157263\pi$
$228$	−0.203136	+	0.758114i	−0.0134530	+	0.0502073i
$229$	−0.832759	+	0.832759i	−0.0550302	+	0.0550302i	−0.734086	−	0.679056i	$-0.762389\pi$
$229$	−0.832759	+	0.832759i	−0.0550302	+	0.0550302i	0.679056	+	0.734086i	$0.262389\pi$
$230$	−1.17747	+	0.679813i	−0.0776402	+	0.0448256i
$231$	3.64247	−	15.2715i	0.239657	−	1.00479i
$232$	6.64833	−	1.78141i	0.436484	−	0.116956i
$233$			6.83577i			0.447826i	0.974609	+	0.223913i	$0.0718832\pi$
$233$			6.83577i			0.447826i	−0.974609	+	0.223913i	$0.928117\pi$
$234$	−0.704879	−	3.53598i	−0.0460794	−	0.231154i
$235$	−33.7233			−2.19986
$236$	5.37683	−	1.44072i	0.350002	−	0.0937828i
$237$	8.01692	+	4.62857i	0.520755	+	0.300658i
$238$	2.62047	+	2.47937i	0.169860	+	0.160714i
$239$	6.87053	−	6.87053i	0.444418	−	0.444418i	−0.449076	−	0.893494i	$-0.648247\pi$
$239$	6.87053	−	6.87053i	0.444418	−	0.444418i	0.893494	+	0.449076i	$0.148247\pi$
$240$	−3.36444	−	0.901498i	−0.217173	−	0.0581915i
$241$	−3.78785	−	1.01495i	−0.243997	−	0.0653787i	0.134748	−	0.990880i	$-0.456978\pi$
$241$	−3.78785	−	1.01495i	−0.243997	−	0.0653787i	−0.378745	+	0.925501i	$0.623644\pi$
$242$	17.1207	+	17.1207i	1.10056	+	1.10056i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−4.84132	+	8.38542i	−0.309934	+	0.536821i
$245$	18.1675	+	16.2609i	1.16068	+	1.03887i
$246$		−	3.61730i		−	0.230630i
$247$	1.86673	+	2.12681i	0.118777	+	0.135326i
$248$		−	0.298656i		−	0.0189647i
$249$	−3.41801	−	12.7562i	−0.216608	−	0.808391i
$250$	6.43152	+	3.71324i	0.406765	+	0.234846i
$251$	−9.97113	−	17.2705i	−0.629372	−	1.09010i	−0.987678	−	0.156500i	$-0.949979\pi$
$251$	−9.97113	−	17.2705i	−0.629372	−	1.09010i	0.358306	−	0.933604i	$-0.383355\pi$
$252$	1.25900	−	2.32700i	0.0793096	−	0.146587i
$253$	2.23739	+	0.599508i	0.140664	+	0.0376907i
$254$	3.37104	−	12.5809i	0.211518	−	0.789395i
$255$	−3.35824	+	3.35824i	−0.210301	+	0.210301i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.32794	+	12.6924i	−0.457105	+	0.791728i	−0.998807	−	0.0488423i	$-0.984447\pi$
$257$	−7.32794	+	12.6924i	−0.457105	+	0.791728i	0.541702	+	0.840571i	$0.317780\pi$
$258$	0.628692	+	2.34631i	0.0391406	+	0.146075i
$259$	−4.57350	−	15.3564i	−0.284183	−	0.954198i
$260$	−9.43859	+	8.28437i	−0.585356	+	0.513775i
$261$	−6.88286			−0.426038
$262$	−21.7465	+	5.82696i	−1.34350	+	0.359991i
$263$	6.28232	−	10.8813i	0.387384	−	0.670969i	−0.604713	−	0.796444i	$-0.706712\pi$
$263$	6.28232	−	10.8813i	0.387384	−	0.670969i	0.992097	+	0.125474i	$0.0400453\pi$
$264$	2.96700	+	5.13899i	0.182606	+	0.316283i
$265$	−23.9813	−	23.9813i	−1.47316	−	1.47316i
$266$	0.0574297	+	2.07574i	0.00352124	+	0.127272i
$267$	1.44141	−	5.37940i	0.0882126	−	0.329214i
$268$	−3.79410	−	3.79410i	−0.231762	−	0.231762i
$269$	18.6795	−	10.7846i	1.13891	−	0.657550i	0.192750	−	0.981248i	$-0.438259\pi$
$269$	18.6795	−	10.7846i	1.13891	−	0.657550i	0.946161	+	0.323698i	$0.104926\pi$
$270$	3.01647	+	1.74156i	0.183577	+	0.105988i
$271$	1.23435	+	4.60664i	0.0749811	+	0.279833i	0.993229	−	0.116173i	$-0.0370626\pi$
$271$	1.23435	+	4.60664i	0.0749811	+	0.279833i	−0.918248	+	0.396006i	$0.870396\pi$
$272$	−1.36351			−0.0826749
$273$	−4.45768	−	8.43381i	−0.269791	−	0.510437i
$274$	−21.3677			−1.29087
$275$	−10.9538	−	40.8800i	−0.660536	−	2.46515i
$276$	0.338051	+	0.195174i	0.0203483	+	0.0117481i
$277$	−23.5013	+	13.5685i	−1.41206	+	0.815251i	−0.995582	−	0.0938963i	$-0.970068\pi$
$277$	−23.5013	+	13.5685i	−1.41206	+	0.815251i	−0.416474	+	0.909147i	$0.636734\pi$
$278$	−10.8089	−	10.8089i	−0.648274	−	0.648274i
$279$	−0.0772979	+	0.288480i	−0.00462770	+	0.0172708i
$280$	−9.21195	+	0.254867i	−0.550519	+	0.0152312i
$281$	−12.1315	−	12.1315i	−0.723704	−	0.723704i	0.245653	−	0.969358i	$-0.420997\pi$
$281$	−12.1315	−	12.1315i	−0.723704	−	0.723704i	−0.969358	+	0.245653i	$0.920997\pi$
$282$	4.84096	+	8.38479i	0.288275	+	0.499307i
$283$	3.51788	−	6.09314i	0.209116	−	0.362200i	−0.742320	−	0.670045i	$-0.766275\pi$
$283$	3.51788	−	6.09314i	0.209116	−	0.362200i	0.951436	+	0.307846i	$0.0996080\pi$
$284$	−12.8877	+	3.45324i	−0.764742	+	0.204912i
$285$	−2.73375			−0.161934
$286$	21.3501	+	1.39044i	1.26246	+	0.0822183i
$287$	−2.73174	−	9.17232i	−0.161249	−	0.541425i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	7.57042	−	13.1124i	0.445319	−	0.771315i
$290$	11.9869	+	20.7619i	0.703896	+	1.21918i
$291$	−9.41911	+	9.41911i	−0.552158	+	0.552158i
$292$	1.86591	−	6.96366i	0.109194	−	0.407517i
$293$	17.9193	+	4.80147i	1.04686	+	0.280505i	0.740953	−	0.671557i	$-0.234374\pi$
$293$	17.9193	+	4.80147i	1.04686	+	0.280505i	0.305906	+	0.952062i	$0.401041\pi$
$294$	1.43511	−	6.85131i	0.0836972	−	0.399577i
$295$	9.69441	+	16.7912i	0.564430	+	0.977622i
$296$	5.24474	+	3.02805i	0.304844	+	0.176002i
$297$	−1.53583	−	5.73180i	−0.0891180	−	0.332593i
$298$			1.25036i			0.0724315i
$299$	1.26201	−	0.623010i	0.0729842	−	0.0360296i
$300$		−	7.13213i		−	0.411774i
$301$	3.36607	+	5.47472i	0.194017	+	0.315558i
$302$	−7.56655	+	13.1056i	−0.435406	+	0.754145i
$303$	−15.3550	+	8.86523i	−0.882123	+	0.509294i
$304$	−0.554978	−	0.554978i	−0.0318302	−	0.0318302i
$305$	−32.5766	−	8.72889i	−1.86533	−	0.499815i
$306$	1.31705	+	0.352902i	0.0752907	+	0.0201741i
$307$	−2.41349	+	2.41349i	−0.137745	+	0.137745i	−0.772617	−	0.634872i	$-0.781053\pi$
$307$	−2.41349	+	2.41349i	−0.137745	+	0.137745i	0.634872	+	0.772617i	$0.281053\pi$
$308$	11.4043	+	10.7902i	0.649819	+	0.614830i
$309$	2.55333	+	1.47417i	0.145254	+	0.0838624i
$310$	1.00481	−	0.269238i	0.0570693	−	0.0152917i
$311$	−3.90589			−0.221483			−0.110741	−	0.993849i	$-0.535323\pi$
$311$	−3.90589			−0.221483			−0.110741	+	0.993849i	$0.535323\pi$
$312$	3.41469	+	1.15755i	0.193319	+	0.0655331i
$313$		−	30.2872i		−	1.71193i	−0.517033	−	0.855966i	$-0.672963\pi$
$313$		−	30.2872i		−	1.71193i	0.517033	−	0.855966i	$-0.327037\pi$
$314$	14.0453	−	3.76342i	0.792620	−	0.212382i
$315$	8.96402	+	2.13804i	0.505065	+	0.120465i
$316$	−8.01692	+	4.62857i	−0.450987	+	0.260377i
$317$	−16.4263	+	16.4263i	−0.922590	+	0.922590i	−0.997212	−	0.0746216i	$-0.976225\pi$
$317$	−16.4263	+	16.4263i	−0.922590	+	0.922590i	0.0746216	+	0.997212i	$0.476225\pi$
$318$	−2.52009	+	9.40511i	−0.141320	+	0.527412i
$319$	10.5709	−	39.4512i	0.591857	−	2.20884i
$320$	2.46294	−	2.46294i	0.137682	−	0.137682i
$321$	−2.37355	+	1.37037i	−0.132479	+	0.0764866i
$322$	1.00458	+	0.239607i	0.0559832	+	0.0133528i
$323$	−1.03370	+	0.276978i	−0.0575164	+	0.0154115i
$324$		−	1.00000i		−	0.0555556i
$325$	−21.3874	−	14.2777i	−1.18636	−	0.791987i
$326$	18.3898			1.01852
$327$	−7.88746	+	2.11344i	−0.436178	+	0.116873i
$328$	3.13267	+	1.80865i	0.172973	+	0.0998659i
$329$	18.6072	+	17.6053i	1.02585	+	0.970613i
$330$	−14.6151	+	14.6151i	−0.804533	+	0.804533i
$331$	−28.9021	−	7.74430i	−1.58860	−	0.425665i	−0.647029	−	0.762466i	$-0.723989\pi$
$331$	−28.9021	−	7.74430i	−1.58860	−	0.425665i	−0.941576	+	0.336800i	$0.890655\pi$
$332$	12.7562	+	3.41801i	0.700088	+	0.187588i
$333$	−4.28231	−	4.28231i	−0.234669	−	0.234669i
$334$	19.9971	−	11.5453i	1.09419	−	0.631733i
$335$	9.34464	−	16.1854i	0.510552	−	0.884302i
$336$	1.38574	+	2.25383i	0.0755982	+	0.122956i
$337$			21.7225i			1.18330i	0.806195	+	0.591650i	$0.201523\pi$
$337$			21.7225i			1.18330i	−0.806195	+	0.591650i	$0.798477\pi$
$338$	10.3070	−	7.92248i	0.560627	−	0.430926i
$339$			6.35108i			0.344943i
$340$	−1.22920	−	4.58744i	−0.0666628	−	0.248789i
$341$	−1.53479	−	0.886112i	−0.0831136	−	0.0479857i
$342$	0.392429	+	0.679706i	0.0212201	+	0.0367543i
$343$	−1.53505	−	18.4565i	−0.0828848	−	0.996559i
$344$	−2.34631	−	0.628692i	−0.126505	−	0.0338968i
$345$	−0.351897	+	1.31330i	−0.0189455	+	0.0707056i
$346$	5.12675	−	5.12675i	0.275616	−	0.275616i
$347$	13.7048	+	23.7374i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$347$	13.7048	+	23.7374i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$348$	3.44143	−	5.96073i	0.184480	−	0.319529i
$349$	2.01381	+	7.51566i	0.107797	+	0.402304i	0.998647	−	0.0519928i	$-0.0165573\pi$
$349$	2.01381	+	7.51566i	0.107797	+	0.402304i	−0.890850	+	0.454297i	$0.849891\pi$
$350$	−5.38610	−	18.0848i	−0.287899	−	0.966675i
$351$	−2.99874	−	2.00189i	−0.160061	−	0.106853i
$352$	−5.93400			−0.316283
$353$	−2.29704	+	0.615489i	−0.122259	+	0.0327592i	−0.319430	−	0.947610i	$-0.603491\pi$
$353$	−2.29704	+	0.615489i	−0.122259	+	0.0327592i	0.197171	+	0.980369i	$0.436825\pi$
$354$	2.78325	−	4.82074i	0.147928	−	0.256219i
$355$	−23.2364	−	40.2466i	−1.23326	−	2.13607i
$356$	3.93799	+	3.93799i	0.208713	+	0.208713i
$357$	3.60613	−	0.0997709i	0.190857	−	0.00528044i
$358$	3.89176	−	14.5243i	0.205686	−	0.767631i
$359$	12.2708	+	12.2708i	0.647629	+	0.647629i	0.952419	−	0.304790i	$-0.0985864\pi$
$359$	12.2708	+	12.2708i	0.647629	+	0.647629i	−0.304790	+	0.952419i	$0.598586\pi$
$360$	−3.01647	+	1.74156i	−0.158982	+	0.0917883i
$361$	15.9210	+	9.19200i	0.837948	+	0.483789i
$362$	2.06250	+	7.69735i	0.108402	+	0.404564i
$363$	24.2123			1.27082
$364$	9.53273	+	0.356440i	0.499651	+	0.0186825i
$365$	25.1109			1.31436
$366$	2.50605	+	9.35272i	0.130993	+	0.488874i
$367$	27.1547	+	15.6778i	1.41747	+	0.818374i	0.996076	−	0.0885060i	$-0.0282092\pi$
$367$	27.1547	+	15.6778i	1.41747	+	0.818374i	0.421389	+	0.906880i	$0.361543\pi$
$368$	−0.338051	+	0.195174i	−0.0176221	+	0.0101741i
$369$	−2.55781	−	2.55781i	−0.133154	−	0.133154i
$370$	−5.45957	+	20.3754i	−0.283829	+	1.05927i
$371$	0.712468	+	25.7515i	0.0369895	+	1.33695i
$372$	−0.211182	−	0.211182i	−0.0109493	−	0.0109493i
$373$	−12.3546	−	21.3987i	−0.639695	−	1.10798i	−0.985500	−	0.169677i	$-0.945727\pi$
$373$	−12.3546	−	21.3987i	−0.639695	−	1.10798i	0.345805	−	0.938306i	$-0.387606\pi$
$374$	−4.04553	+	7.00707i	−0.209189	+	0.362327i
$375$	7.17343	−	1.92211i	0.370434	−	0.0992575i
$376$	−9.68192			−0.499307
$377$	−10.9853	−	22.2527i	−0.565773	−	1.14607i
$378$	−0.755188	−	2.53568i	−0.0388427	−	0.130421i
$379$	4.75813	+	17.7576i	0.244409	+	0.912145i	0.973680	+	0.227921i	$0.0731927\pi$
$379$	4.75813	+	17.7576i	0.244409	+	0.912145i	−0.729271	+	0.684225i	$0.760141\pi$
$380$	1.36688	−	2.36750i	0.0701193	−	0.121450i
$381$	−6.51235	−	11.2797i	−0.333638	−	0.577877i
$382$	6.27236	−	6.27236i	0.320922	−	0.320922i
$383$	−2.50600	+	9.35251i	−0.128051	+	0.477891i	−0.999930	−	0.0118294i	$-0.996234\pi$
$383$	−2.50600	+	9.35251i	−0.128051	+	0.477891i	0.871880	+	0.489720i	$0.162901\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−26.0221	+	48.0963i	−1.32621	+	2.45122i
$386$	1.83581	+	3.17971i	0.0934402	+	0.161843i
$387$	2.10364	+	1.21454i	0.106934	+	0.0617385i
$388$	−3.44763	−	12.8667i	−0.175027	−	0.653210i
$389$			13.3041i			0.674545i	0.941407	+	0.337272i	$0.109504\pi$
$389$			13.3041i			0.674545i	−0.941407	+	0.337272i	$0.890496\pi$
$390$	−0.816156	+	12.5320i	−0.0413276	+	0.634584i
$391$			0.532242i			0.0269167i
$392$	5.21586	+	4.66850i	0.263441	+	0.235795i
$393$	−11.2568	+	19.4974i	−0.567831	+	0.983512i
$394$	−13.0503	+	7.53457i	−0.657463	+	0.379586i
$395$	−22.7998	−	22.7998i	−1.14718	−	1.14718i
$396$	5.73180	+	1.53583i	0.288034	+	0.0771784i
$397$	−20.2162	−	5.41692i	−1.01462	−	0.271868i	−0.287064	−	0.957912i	$-0.592679\pi$
$397$	−20.2162	−	5.41692i	−1.01462	−	0.271868i	−0.727560	+	0.686044i	$0.759346\pi$
$398$	−6.08899	+	6.08899i	−0.305213	+	0.305213i
$399$	1.50838	+	1.42716i	0.0755135	+	0.0714475i
$400$	6.17661	+	3.56607i	0.308830	+	0.178303i
$401$	−11.8638	+	3.17888i	−0.592448	+	0.158746i	−0.542572	−	0.840010i	$-0.682549\pi$
$401$	−11.8638	+	3.17888i	−0.592448	+	0.158746i	−0.0498760	+	0.998755i	$0.515883\pi$
$402$	−5.36567			−0.267615
$403$	−1.05604	+	0.210517i	−0.0526052	+	0.0104866i
$404$		−	17.7305i		−	0.882123i
$405$	3.36444	−	0.901498i	0.167180	−	0.0447958i
$406$	4.22491	−	17.7135i	0.209679	−	0.879104i
$407$	31.1223	−	17.9685i	1.54267	−	0.890663i
$408$	−0.964147	+	0.964147i	−0.0477324	+	0.0477324i
$409$	−1.07120	+	3.99778i	−0.0529675	+	0.197677i	−0.987339	−	0.158622i	$-0.949295\pi$
$409$	−1.07120	+	3.99778i	−0.0529675	+	0.197677i	0.934372	+	0.356299i	$0.115962\pi$
$410$	−3.26098	+	12.1702i	−0.161049	+	0.601041i
$411$	−15.1092	+	15.1092i	−0.745284	+	0.745284i
$412$	−2.55333	+	1.47417i	−0.125794	+	0.0726269i
$413$	3.41689	−	14.3257i	0.168134	−	0.704924i
$414$	0.377047	−	0.101029i	0.0185308	−	0.00496532i
$415$			45.9988i			2.25799i
$416$	−2.70981	+	2.37843i	−0.132859	+	0.116612i
$417$	−15.2861			−0.748562
$418$	−4.49865	+	1.20541i	−0.220036	+	0.0589584i
$419$	26.8922	+	15.5262i	1.31377	+	0.758504i	0.982718	−	0.185109i	$-0.0592639\pi$
$419$	26.8922	+	15.5262i	1.31377	+	0.758504i	0.331050	+	0.943613i	$0.392597\pi$
$420$	−6.33361	+	6.69405i	−0.309049	+	0.326636i
$421$	23.7904	−	23.7904i	1.15947	−	1.15947i	0.174882	−	0.984589i	$-0.444046\pi$
$421$	23.7904	−	23.7904i	1.15947	−	1.15947i	0.984589	−	0.174882i	$-0.0559545\pi$
$422$	−4.75950	−	1.27530i	−0.231689	−	0.0620808i
$423$	9.35201	+	2.50586i	0.454710	+	0.121839i
$424$	−6.88502	−	6.88502i	−0.334366	−	0.334366i
$425$	8.42187	−	4.86237i	0.408520	−	0.235859i
$426$	−6.67114	+	11.5548i	−0.323218	+	0.559830i
$427$	13.4176	+	21.8230i	0.649324	+	1.05609i
$428$		−	2.74074i		−	0.132479i
$429$	16.0800	−	14.1136i	0.776349	−	0.681412i
$430$		−	8.46077i		−	0.408015i
$431$	2.38619	+	8.90540i	0.114939	+	0.428958i	0.999282	−	0.0378790i	$-0.0120601\pi$
$431$	2.38619	+	8.90540i	0.114939	+	0.428958i	−0.884343	+	0.466837i	$0.845393\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	9.06647	+	15.7036i	0.435707	+	0.754666i	0.997353	−	0.0727111i	$-0.0231651\pi$
$433$	9.06647	+	15.7036i	0.435707	+	0.754666i	−0.561646	+	0.827378i	$0.689832\pi$
$434$	−0.694972	−	0.376008i	−0.0333597	−	0.0180490i
$435$	23.1569	+	6.20488i	1.11029	+	0.297501i
$436$	2.11344	−	7.88746i	0.101215	−	0.377741i
$437$	−0.216634	+	0.216634i	−0.0103630	+	0.0103630i
$438$	−3.60466	−	6.24345i	−0.172237	−	0.298323i
$439$	−17.0376	+	29.5100i	−0.813160	+	1.40844i	0.0974810	+	0.995237i	$0.468921\pi$
$439$	−17.0376	+	29.5100i	−0.813160	+	1.40844i	−0.910641	+	0.413198i	$0.864412\pi$
$440$	−5.34949	−	19.9646i	−0.255027	−	0.951773i
$441$	−3.82983	−	5.85938i	−0.182373	−	0.279018i
$442$	0.961110	+	4.82134i	0.0457153	+	0.229328i
$443$	−37.1553			−1.76530			−0.882650	−	0.470030i	$-0.844243\pi$
$443$	−37.1553			−1.76530			−0.882650	+	0.470030i	$0.844243\pi$
$444$	5.84975	−	1.56744i	0.277617	−	0.0743872i
$445$	−9.69904	+	16.7992i	−0.459778	+	0.796360i
$446$	−5.85659	−	10.1439i	−0.277318	−	0.480328i
$447$	0.884139	+	0.884139i	0.0418183	+	0.0418183i
$448$	−2.64474	+	0.0731721i	−0.124952	+	0.00345706i
$449$	3.12913	−	11.6781i	0.147673	−	0.551122i	−0.851949	−	0.523625i	$-0.824579\pi$
$449$	3.12913	−	11.6781i	0.147673	−	0.551122i	0.999622	−	0.0274976i	$-0.00875387\pi$
$450$	−5.04318	−	5.04318i	−0.237738	−	0.237738i
$451$	18.5893	−	10.7325i	0.875334	−	0.505374i
$452$	−5.50020	−	3.17554i	−0.258708	−	0.149365i
$453$	3.91673	+	14.6174i	0.184024	+	0.686787i
$454$	−6.93585			−0.325516
$455$	7.39452	+	32.3936i	0.346660	+	1.51864i
$456$	−0.784857			−0.0367543
$457$	−1.71247	−	6.39104i	−0.0801061	−	0.298960i	0.914236	−	0.405181i	$-0.132792\pi$
$457$	−1.71247	−	6.39104i	−0.0801061	−	0.298960i	−0.994343	+	0.106221i	$0.966125\pi$
$458$	−1.01992	−	0.588849i	−0.0476576	−	0.0275151i
$459$	1.18083	−	0.681755i	0.0551166	−	0.0318216i
$460$	−0.961401	−	0.961401i	−0.0448256	−	0.0448256i
$461$	−6.00819	+	22.4229i	−0.279829	+	1.04434i	0.672706	+	0.739909i	$0.265132\pi$
$461$	−6.00819	+	22.4229i	−0.279829	+	1.04434i	−0.952536	+	0.304427i	$0.901535\pi$
$462$	15.6939	−	0.434203i	0.730145	−	0.0202010i
$463$	−4.55758	−	4.55758i	−0.211809	−	0.211809i	0.593227	−	0.805035i	$-0.297854\pi$
$463$	−4.55758	−	4.55758i	−0.211809	−	0.211809i	−0.805035	+	0.593227i	$0.797854\pi$
$464$	3.44143	+	5.96073i	0.159764	+	0.276720i
$465$	0.520128	−	0.900888i	0.0241203	−	0.0417777i
$466$	−6.60285	+	1.76923i	−0.305871	+	0.0819579i
$467$	11.0261			0.510228			0.255114	−	0.966911i	$-0.417887\pi$
$467$	11.0261			0.510228			0.255114	+	0.966911i	$0.417887\pi$
$468$	3.23306	−	1.59604i	0.149448	−	0.0737770i
$469$	−13.6056	+	4.05209i	−0.628250	+	0.187108i
$470$	−8.72823	−	32.5742i	−0.402603	−	1.50254i
$471$	7.27036	−	12.5926i	0.335001	−	0.580238i
$472$	2.78325	+	4.82074i	0.128110	+	0.221892i
$473$	−10.1923	+	10.1923i	−0.468644	+	0.468644i
$474$	−2.39592	+	8.94171i	−0.110048	+	0.410706i
$475$	5.40697	+	1.44879i	0.248089	+	0.0664752i
$476$	−1.71666	+	3.17288i	−0.0786830	+	0.145429i
$477$	4.86844	+	8.43239i	0.222911	+	0.386093i
$478$	8.41465	+	4.85820i	0.384877	+	0.222209i
$479$	−1.58884	−	5.92965i	−0.0725961	−	0.270932i	0.920081	−	0.391727i	$-0.128122\pi$
$479$	−1.58884	−	5.92965i	−0.0725961	−	0.270932i	−0.992677	+	0.120795i	$0.961456\pi$
$480$		−	3.48312i		−	0.158982i
$481$	7.01022	−	20.6797i	0.319638	−	0.942913i
$482$		−	3.92147i		−	0.178618i
$483$	0.879775	−	0.540919i	0.0400311	−	0.0246127i
$484$	−12.1062	+	20.9685i	−0.550280	+	0.953113i
$485$	40.1813	−	23.1987i	1.82454	−	1.05340i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	10.5482	+	2.82637i	0.477983	+	0.128075i	0.489763	−	0.871855i	$-0.337083\pi$
$487$	10.5482	+	2.82637i	0.477983	+	0.128075i	−0.0117801	+	0.999931i	$0.503750\pi$
$488$	−9.35272	−	2.50605i	−0.423378	−	0.113444i
$489$	13.0036	−	13.0036i	0.588042	−	0.588042i
$490$	−11.0048	+	21.7571i	−0.497145	+	0.982884i
$491$	−7.10942	−	4.10463i	−0.320844	−	0.185239i	0.330925	−	0.943657i	$-0.392639\pi$
$491$	−7.10942	−	4.10463i	−0.320844	−	0.185239i	−0.651769	+	0.758418i	$0.725973\pi$
$492$	3.49404	−	0.936225i	0.157523	−	0.0422083i
$493$	9.38485			0.422672
$494$	−1.57120	+	2.35358i	−0.0706915	+	0.105893i
$495$			20.6688i			0.928995i
$496$	0.288480	−	0.0772979i	0.0129531	−	0.00347078i
$497$	−8.18989	+	34.3372i	−0.367367	+	1.54023i
$498$	11.4369	−	6.60310i	0.512500	−	0.295892i
$499$	24.2077	−	24.2077i	1.08369	−	1.08369i	0.0875246	−	0.996162i	$-0.472104\pi$
$499$	24.2077	−	24.2077i	1.08369	−	1.08369i	0.996162	−	0.0875246i	$-0.0278957\pi$
$500$	−1.92211	+	7.17343i	−0.0859595	+	0.320805i
$501$	5.97631	−	22.3039i	0.267002	−	0.996464i
$502$	14.1013	−	14.1013i	0.629372	−	0.629372i
$503$	−8.94037	+	5.16172i	−0.398631	+	0.230150i	−0.685893	−	0.727702i	$-0.740588\pi$
$503$	−8.94037	+	5.16172i	−0.398631	+	0.230150i	0.287262	+	0.957852i	$0.407255\pi$
$504$	2.57356	+	0.613830i	0.114635	+	0.0273422i
$505$	59.6530	−	15.9840i	2.65452	−	0.711277i
$506$			2.31632i			0.102973i
$507$	1.68611	−	12.8902i	0.0748830	−	0.572473i
$508$	13.0247			0.577877
$509$	18.5789	−	4.97820i	0.823495	−	0.220655i	0.177621	−	0.984099i	$-0.443160\pi$
$509$	18.5789	−	4.97820i	0.823495	−	0.220655i	0.645874	+	0.763444i	$0.276493\pi$
$510$	−4.11299	−	2.37463i	−0.182126	−	0.105151i
$511$	−13.8552	−	13.1092i	−0.612920	−	0.579917i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.758114	+	0.203136i	0.0334715	+	0.00896867i
$514$	−14.1565	−	3.79322i	−0.624416	−	0.167312i
$515$	−7.26156	−	7.26156i	−0.319983	−	0.319983i
$516$	−2.10364	+	1.21454i	−0.0926078	+	0.0534671i
$517$	−28.7262	+	49.7553i	−1.26338	+	2.18824i
$518$	13.6494	−	8.39218i	0.599720	−	0.368731i
$519$		−	7.25031i		−	0.318253i
$520$	−10.4450	−	6.97282i	−0.458042	−	0.305779i
$521$			39.9065i			1.74833i	0.485625	+	0.874167i	$0.338592\pi$
$521$			39.9065i			1.74833i	−0.485625	+	0.874167i	$0.661408\pi$
$522$	−1.78141	−	6.64833i	−0.0779704	−	0.290990i
$523$	−8.17412	−	4.71933i	−0.357429	−	0.206362i	0.310523	−	0.950566i	$-0.399496\pi$
$523$	−8.17412	−	4.71933i	−0.357429	−	0.206362i	−0.667953	+	0.744204i	$0.732829\pi$
$524$	−11.2568	−	19.4974i	−0.491756	−	0.851747i
$525$	−16.5965	−	8.97936i	−0.724329	−	0.391891i
$526$	12.1365	+	3.25197i	0.529177	+	0.141793i
$527$	0.105396	−	0.393345i	0.00459114	−	0.0171344i
$528$	−4.19597	+	4.19597i	−0.182606	+	0.182606i
$529$	−11.4238	−	19.7866i	−0.496688	−	0.860288i
$530$	16.9574	−	29.3710i	0.736581	−	1.27580i
$531$	−1.44072	−	5.37683i	−0.0625219	−	0.233335i
$532$	−1.99015	+	0.592715i	−0.0862839	+	0.0256974i
$533$	4.18719	−	12.3519i	0.181367	−	0.535022i
$534$	5.56916			0.241001
$535$	9.22104	−	2.47077i	0.398661	−	0.106821i
$536$	2.68284	−	4.64681i	0.115881	−	0.200712i
$537$	−7.51831	−	13.0221i	−0.324439	−	0.561945i
$538$	15.2518	+	15.2518i	0.657550	+	0.657550i
$539$	39.4668	−	12.9528i	1.69996	−	0.557918i
$540$	−0.901498	+	3.36444i	−0.0387943	+	0.144782i
$541$	11.1738	+	11.1738i	0.480397	+	0.480397i	0.905259	−	0.424861i	$-0.139677\pi$
$541$	11.1738	+	11.1738i	0.480397	+	0.480397i	−0.424861	+	0.905259i	$0.639677\pi$
$542$	−4.13020	+	2.38457i	−0.177407	+	0.102426i
$543$	6.90125	+	3.98444i	0.296161	+	0.170989i
$544$	−0.352902	−	1.31705i	−0.0151306	−	0.0564680i
$545$	28.4421			1.21833
$546$	6.99270	−	6.48862i	0.299260	−	0.277687i
$547$	3.67435			0.157104			0.0785519	−	0.996910i	$-0.474970\pi$
$547$	3.67435			0.157104			0.0785519	+	0.996910i	$0.474970\pi$
$548$	−5.53036	−	20.6396i	−0.236245	−	0.881680i
$549$	8.38542	+	4.84132i	0.357881	+	0.206623i
$550$	36.6520	−	21.1610i	1.56285	−	0.902309i
$551$	3.81983	+	3.81983i	0.162730	+	0.162730i
$552$	−0.101029	+	0.377047i	−0.00430009	+	0.0160482i
$553$	0.677365	+	24.4827i	0.0288045	+	1.04111i
$554$	−19.1887	−	19.1887i	−0.815251	−	0.815251i
$555$	10.5471	+	18.2681i	0.447698	+	0.775436i
$556$	7.64304	−	13.2381i	0.324137	−	0.561422i
$557$	−1.80798	+	0.484446i	−0.0766065	+	0.0205267i	−0.296919	−	0.954903i	$-0.595959\pi$
$557$	−1.80798	+	0.484446i	−0.0766065	+	0.0205267i	0.220312	+	0.975429i	$0.429292\pi$
$558$	−0.298656			−0.0126431
$559$	−0.569175	+	8.73965i	−0.0240735	+	0.369648i
$560$	−2.63041	−	8.83209i	−0.111155	−	0.373224i
$561$	2.09412	+	7.81537i	0.0884139	+	0.329965i
$562$	8.57826	−	14.8580i	0.361852	−	0.626746i
$563$	−0.329848	−	0.571314i	−0.0139014	−	0.0240780i	0.858991	−	0.511991i	$-0.171092\pi$
$563$	−0.329848	−	0.571314i	−0.0139014	−	0.0240780i	−0.872892	+	0.487913i	$0.837758\pi$
$564$	−6.84615	+	6.84615i	−0.288275	+	0.288275i
$565$	5.72549	−	21.3678i	0.240873	−	0.898951i
$566$	6.79602	+	1.82099i	0.285658	+	0.0765418i
$567$	−2.32700	−	1.25900i	−0.0977247	−	0.0528731i
$568$	−6.67114	−	11.5548i	−0.279915	−	0.484827i
$569$	19.3083	+	11.1477i	0.809446	+	0.467334i	0.846764	−	0.531969i	$-0.178548\pi$
$569$	19.3083	+	11.1477i	0.809446	+	0.467334i	−0.0373172	+	0.999303i	$0.511881\pi$
$570$	−0.707547	−	2.64060i	−0.0296359	−	0.110603i
$571$			5.98049i			0.250276i	0.992139	+	0.125138i	$0.0399373\pi$
$571$			5.98049i			0.250276i	−0.992139	+	0.125138i	$0.960063\pi$
$572$	4.18275	+	20.9825i	0.174890	+	0.877322i
$573$		−	8.87046i		−	0.370569i
$574$	8.15275	−	5.01263i	0.340289	−	0.209223i
$575$	1.39200	−	2.41102i	0.0580506	−	0.100547i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−7.43677	−	7.43677i	−0.309597	−	0.309597i	0.535156	−	0.844753i	$-0.320253\pi$
$577$	−7.43677	−	7.43677i	−0.309597	−	0.309597i	−0.844753	+	0.535156i	$0.820253\pi$
$578$	14.6249	+	3.91874i	0.608317	+	0.162998i
$579$	3.54651	+	0.950284i	0.147388	+	0.0394925i
$580$	−16.9521	+	16.9521i	−0.703896	+	0.703896i
$581$	24.0138	−	25.3804i	0.996259	−	1.05296i
$582$	−11.5360	−	6.66032i	−0.478183	−	0.276079i
$583$	−55.8099	+	14.9542i	−2.31141	+	0.619340i
$584$	7.20931			0.298323
$585$	8.28437	+	9.43859i	0.342517	+	0.390238i
$586$			18.5515i			0.766354i
$587$	−21.0591	+	5.64276i	−0.869201	+	0.232902i	−0.665742	−	0.746182i	$-0.731885\pi$
$587$	−21.0591	+	5.64276i	−0.869201	+	0.232902i	−0.203459	+	0.979083i	$0.565218\pi$
$588$	6.98929	−	0.387042i	0.288234	−	0.0159614i
$589$	0.202998	−	0.117201i	0.00836440	−	0.00482919i
$590$	−13.7100	+	13.7100i	−0.564430	+	0.564430i
$591$	−3.90018	+	14.5557i	−0.160432	+	0.598741i
$592$	−1.56744	+	5.84975i	−0.0644212	+	0.240423i
$593$	−31.6701	+	31.6701i	−1.30054	+	1.30054i	−0.372508	+	0.928029i	$0.621502\pi$
$593$	−31.6701	+	31.6701i	−1.30054	+	1.30054i	−0.928029	+	0.372508i	$0.878498\pi$
$594$	5.13899	−	2.96700i	0.210855	−	0.121737i
$595$	−12.2225	−	2.91524i	−0.501075	−	0.119513i
$596$	−1.20776	+	0.323617i	−0.0494716	+	0.0132559i
$597$			8.61113i			0.352430i
$598$	0.928415	+	1.05777i	0.0379657	+	0.0432553i
$599$	23.5065			0.960451			0.480226	−	0.877145i	$-0.340555\pi$
$599$	23.5065			0.960451			0.480226	+	0.877145i	$0.340555\pi$
$600$	6.88911	−	1.84593i	0.281247	−	0.0753598i
$601$	−41.2432	−	23.8118i	−1.68234	−	0.971302i	−0.960097	−	0.279666i	$-0.909776\pi$
$601$	−41.2432	−	23.8118i	−1.68234	−	0.971302i	−0.722247	−	0.691636i	$-0.756890\pi$
$602$	−4.41697	+	4.66833i	−0.180022	+	0.190267i
$603$	−3.79410	+	3.79410i	−0.154508	+	0.154508i
$604$	−14.6174	−	3.91673i	−0.594775	−	0.159370i
$605$	−81.4608	−	21.8274i	−3.31185	−	0.887408i
$606$	−12.5373	−	12.5373i	−0.509294	−	0.509294i
$607$	1.65889	−	0.957758i	0.0673321	−	0.0388742i	−0.465956	−	0.884808i	$-0.654290\pi$
$607$	1.65889	−	0.957758i	0.0673321	−	0.0388742i	0.533288	+	0.845934i	$0.320956\pi$
$608$	0.392429	−	0.679706i	0.0159151	−	0.0275657i
$609$	−9.53784	−	15.5128i	−0.386493	−	0.628609i
$610$		−	33.7258i		−	1.36552i
$611$	6.82458	+	34.2351i	0.276093	+	1.38500i
$612$			1.36351i			0.0551166i
$613$	−0.684906	−	2.55611i	−0.0276631	−	0.103240i	0.950714	−	0.310069i	$-0.100352\pi$
$613$	−0.684906	−	2.55611i	−0.0276631	−	0.103240i	−0.978377	+	0.206829i	$0.933686\pi$
$614$	−2.95591	−	1.70659i	−0.119291	−	0.0688725i
$615$	6.29974	+	10.9115i	0.254030	+	0.439993i
$616$	−7.47091	+	13.8084i	−0.301011	+	0.556356i
$617$	−3.04305	−	0.815383i	−0.122509	−	0.0328261i	0.197044	−	0.980395i	$-0.436866\pi$
$617$	−3.04305	−	0.815383i	−0.122509	−	0.0328261i	−0.319552	+	0.947569i	$0.603533\pi$
$618$	−0.763084	+	2.84787i	−0.0306958	+	0.114558i
$619$	23.7062	−	23.7062i	0.952831	−	0.952831i	−0.0461053	−	0.998937i	$-0.514681\pi$
$619$	23.7062	−	23.7062i	0.952831	−	0.952831i	0.998937	+	0.0461053i	$0.0146810\pi$
$620$	0.520128	+	0.900888i	0.0208888	+	0.0361805i
$621$	0.195174	−	0.338051i	0.00783205	−	0.0135655i
$622$	−1.01092	−	3.77280i	−0.0405342	−	0.151276i
$623$	14.1216	−	4.20576i	0.565772	−	0.168500i
$624$	−0.234317	+	3.59793i	−0.00938020	+	0.144032i
$625$	9.79335			0.391734
$626$	29.2551	−	7.83889i	1.16927	−	0.313305i
$627$	−2.32867	+	4.03337i	−0.0929981	+	0.161077i
$628$	7.27036	+	12.5926i	0.290119	+	0.502501i
$629$	5.83897	+	5.83897i	0.232815	+	0.232815i
$630$	0.254867	+	9.21195i	0.0101542	+	0.367013i
$631$	0.430633	−	1.60714i	0.0171432	−	0.0639794i	−0.956824	−	0.290667i	$-0.906123\pi$
$631$	0.430633	−	1.60714i	0.0171432	−	0.0639794i	0.973968	+	0.226687i	$0.0727896\pi$
$632$	−6.54579	−	6.54579i	−0.260377	−	0.260377i
$633$	−4.26725	+	2.46370i	−0.169608	+	0.0979231i
$634$	−20.1180	−	11.6151i	−0.798987	−	0.461295i
$635$	11.7417	+	43.8208i	0.465957	+	1.73897i
$636$	−9.73688			−0.386093
$637$	12.8311	−	21.7339i	0.508389	−	0.861128i
$638$	40.8429			1.61698
$639$	3.45324	+	12.8877i	0.136608	+	0.509828i
$640$	3.01647	+	1.74156i	0.119237	+	0.0688412i
$641$	−10.3277	+	5.96272i	−0.407921	+	0.235513i	−0.689896	−	0.723908i	$-0.742344\pi$
$641$	−10.3277	+	5.96272i	−0.407921	+	0.235513i	0.281975	+	0.959422i	$0.409010\pi$
$642$	−1.93800	−	1.93800i	−0.0764866	−	0.0764866i
$643$	6.28890	−	23.4705i	0.248010	−	0.925585i	−0.723837	−	0.689971i	$-0.757623\pi$
$643$	6.28890	−	23.4705i	0.248010	−	0.925585i	0.971847	−	0.235614i	$-0.0757102\pi$
$644$	0.0285625	+	1.03237i	0.00112552	+	0.0406809i
$645$	−5.98267	−	5.98267i	−0.235567	−	0.235567i
$646$	−0.535080	−	0.926786i	−0.0210525	−	0.0364639i
$647$	−22.1120	+	38.2991i	−0.869312	+	1.50569i	−0.00661029	+	0.999978i	$0.502104\pi$
$647$	−22.1120	+	38.2991i	−0.869312	+	1.50569i	−0.862701	+	0.505714i	$0.831229\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	33.0316			1.29661
$650$	8.25577	−	24.3540i	0.323818	−	0.955243i
$651$	−0.757297	+	0.225541i	−0.0296808	+	0.00883967i
$652$	4.75964	+	17.7632i	0.186402	+	0.695662i
$653$	−8.80949	+	15.2585i	−0.344742	+	0.597111i	−0.985307	−	0.170793i	$-0.945367\pi$
$653$	−8.80949	+	15.2585i	−0.344742	+	0.597111i	0.640565	+	0.767904i	$0.278700\pi$
$654$	−4.08285	−	7.07171i	−0.159652	−	0.276526i
$655$	55.4497	−	55.4497i	2.16660	−	2.16660i
$656$	−0.936225	+	3.49404i	−0.0365534	+	0.136419i
$657$	−6.96366	−	1.86591i	−0.271678	−	0.0727960i
$658$	−12.1895	+	22.5298i	−0.475198	+	0.878303i
$659$	−19.7135	−	34.1447i	−0.767928	−	1.33009i	−0.938685	−	0.344777i	$-0.887955\pi$
$659$	−19.7135	−	34.1447i	−0.767928	−	1.33009i	0.170757	−	0.985313i	$-0.445379\pi$
$660$	−17.8997	−	10.3344i	−0.696746	−	0.402267i
$661$	2.09098	+	7.80365i	0.0813297	+	0.303527i	0.994594	−	0.103841i	$-0.0331134\pi$
$661$	2.09098	+	7.80365i	0.0813297	+	0.303527i	−0.913264	+	0.407368i	$0.866447\pi$
$662$		−	29.9217i		−	1.16294i
$663$	4.08881	+	2.72960i	0.158796	+	0.106009i
$664$			13.2062i			0.512500i
$665$	−3.78827	−	6.16140i	−0.146903	−	0.238929i
$666$	3.02805	−	5.24474i	0.117335	−	0.203230i
$667$	2.32675	−	1.34335i	0.0900923	−	0.0520148i
$668$	16.3276	+	16.3276i	0.631733	+	0.631733i
$669$	−11.3141	−	3.03159i	−0.437427	−	0.117208i
$670$	18.0525	+	4.83714i	0.697427	+	0.186875i
$671$	−40.6281	+	40.6281i	−1.56843	+	1.56843i
$672$	−1.81837	+	1.92185i	−0.0701452	+	0.0741371i
$673$	20.2298	+	11.6797i	0.779803	+	0.450219i	0.836360	−	0.548180i	$-0.184679\pi$
$673$	20.2298	+	11.6797i	0.779803	+	0.450219i	−0.0565577	+	0.998399i	$0.518012\pi$
$674$	−20.9823	+	5.62220i	−0.808209	+	0.216559i
$675$	−7.13213			−0.274516
$676$	10.3202	+	7.90531i	0.396930	+	0.304051i
$677$			42.4364i			1.63097i	0.578782	+	0.815483i	$0.303528\pi$
$677$			42.4364i			1.63097i	−0.578782	+	0.815483i	$0.696472\pi$
$678$	−6.13467	+	1.64378i	−0.235601	+	0.0631290i
$679$	−34.2815	−	8.17661i	−1.31560	−	0.313789i
$680$	4.11299	−	2.37463i	0.157726	−	0.0910631i
$681$	−4.90439	+	4.90439i	−0.187936	+	0.187936i
$682$	0.458685	−	1.71184i	0.0175640	−	0.0655496i
$683$	3.84079	−	14.3340i	0.146964	−	0.548476i	−0.852696	−	0.522407i	$-0.825034\pi$
$683$	3.84079	−	14.3340i	0.146964	−	0.548476i	0.999660	−	0.0260692i	$-0.00829902\pi$
$684$	−0.554978	+	0.554978i	−0.0212201	+	0.0212201i
$685$	64.4550	−	37.2131i	2.46270	−	1.42184i
$686$	17.4303	−	6.25964i	0.665494	−	0.238994i
$687$	−1.13757	+	0.304811i	−0.0434010	+	0.0116293i
$688$		−	2.42908i		−	0.0926078i
$689$	−19.4922	+	29.1984i	−0.742592	+	1.11237i
$690$	−1.35963			−0.0517601
$691$	41.4261	−	11.1001i	1.57592	−	0.422267i	0.638261	−	0.769820i	$-0.279654\pi$
$691$	41.4261	−	11.1001i	1.57592	−	0.422267i	0.937660	+	0.347553i	$0.112987\pi$
$692$	6.27896	+	3.62516i	0.238690	+	0.137808i
$693$	10.7902	−	11.4043i	0.409886	−	0.433213i
$694$	−19.3815	+	19.3815i	−0.735712	+	0.735712i
$695$	51.4290	+	13.7804i	1.95081	+	0.522719i
$696$	6.64833	+	1.78141i	0.252004	+	0.0675244i
$697$	3.48760	+	3.48760i	0.132102	+	0.132102i
$698$	−6.73835	+	3.89039i	−0.255050	+	0.147253i
$699$	−3.41788	+	5.91995i	−0.129276	+	0.223913i
$700$	16.0746	−	9.88327i	0.607562	−	0.373553i
$701$		−	21.6520i		−	0.817783i	−0.912583	−	0.408892i	$-0.865915\pi$
$701$		−	21.6520i		−	0.817783i	0.912583	−	0.408892i	$-0.134085\pi$
$702$	1.15755	−	3.41469i	0.0436888	−	0.128879i
$703$			4.75318i			0.179269i
$704$	−1.53583	−	5.73180i	−0.0578838	−	0.216025i
$705$	−29.2052	−	16.8616i	−1.09993	−	0.635046i
$706$	−1.18903	−	2.05947i	−0.0447499	−	0.0775091i
$707$	−41.2587	−	22.3227i	−1.55169	−	0.839530i
$708$	5.37683	+	1.44072i	0.202074	+	0.0541455i
$709$	−3.84427	+	14.3470i	−0.144375	+	0.538813i	0.855408	+	0.517955i	$0.173307\pi$
$709$	−3.84427	+	14.3470i	−0.144375	+	0.538813i	−0.999782	+	0.0208583i	$0.993360\pi$
$710$	32.8612	−	32.8612i	1.23326	−	1.23326i
$711$	4.62857	+	8.01692i	0.173585	+	0.300658i
$712$	−2.78458	+	4.82304i	−0.104357	+	0.180751i
$713$	−0.0301730	−	0.112607i	−0.00112999	−	0.00421717i
$714$	1.02971	+	3.45743i	0.0385358	+	0.129391i
$715$	−66.8235	+	32.9883i	−2.49906	+	1.23369i
$716$	15.0366			0.561945
$717$	9.38532	−	2.51479i	0.350501	−	0.0939165i
$718$	−8.67678	+	15.0286i	−0.323814	+	0.560863i
$719$	−19.3705	−	33.5507i	−0.722399	−	1.25123i	−0.960036	−	0.279877i	$-0.909706\pi$
$719$	−19.3705	−	33.5507i	−0.722399	−	1.25123i	0.237637	−	0.971354i	$-0.423627\pi$
$720$	−2.46294	−	2.46294i	−0.0917883	−	0.0917883i
$721$	0.215736	+	7.79757i	0.00803442	+	0.290397i
$722$	−4.75813	+	17.7576i	−0.177079	+	0.660869i
$723$	−2.77290	−	2.77290i	−0.103125	−	0.103125i
$724$	−6.90125	+	3.98444i	−0.256483	+	0.148081i
$725$	−42.5127	−	24.5447i	−1.57888	−	0.911568i
$726$	6.26661	+	23.3873i	0.232576	+	0.867984i
$727$	−9.19936			−0.341186			−0.170593	−	0.985342i	$-0.554568\pi$
$727$	−9.19936			−0.341186			−0.170593	+	0.985342i	$0.554568\pi$
$728$	2.12296	+	9.30016i	0.0786820	+	0.344687i
$729$	−1.00000			−0.0370370
$730$	6.49918	+	24.2553i	0.240545	+	0.897728i
$731$	−2.86834	−	1.65604i	−0.106089	−	0.0612507i
$732$	−8.38542	+	4.84132i	−0.309934	+	0.178940i
$733$	26.3545	+	26.3545i	0.973426	+	0.973426i	0.999656	−	0.0262295i	$-0.00835007\pi$
$733$	26.3545	+	26.3545i	0.973426	+	0.973426i	−0.0262295	+	0.999656i	$0.508350\pi$
$734$	−8.11542	+	30.2872i	−0.299546	+	1.11792i
$735$	7.60301	+	23.1661i	0.280441	+	0.854495i
$736$	−0.276017	−	0.276017i	−0.0101741	−	0.0101741i
$737$	−15.9199	−	27.5741i	−0.586418	−	1.01571i
$738$	1.80865	−	3.13267i	0.0665772	−	0.115315i
$739$	10.3275	−	2.76726i	0.379905	−	0.101795i	−0.0638126	−	0.997962i	$-0.520326\pi$
$739$	10.3275	−	2.76726i	0.379905	−	0.101795i	0.443718	+	0.896167i	$0.353659\pi$
$740$	−21.0941			−0.775436
$741$	0.553230	+	2.77524i	0.0203234	+	0.101951i
$742$	−24.6897	+	7.35317i	−0.906386	+	0.269944i
$743$	7.78997	+	29.0726i	0.285786	+	1.06657i	0.948263	+	0.317486i	$0.102839\pi$
$743$	7.78997	+	29.0726i	0.285786	+	1.06657i	−0.662477	+	0.749083i	$0.730495\pi$
$744$	0.149328	−	0.258644i	0.00547463	−	0.00948234i
$745$	−2.17758	−	3.77168i	−0.0797804	−	0.138184i
$746$	17.4720	−	17.4720i	0.639695	−	0.639695i
$747$	3.41801	−	12.7562i	0.125059	−	0.466725i
$748$	−7.81537	−	2.09412i	−0.285758	−	0.0765687i
$749$	−6.37769	−	3.45059i	−0.233036	−	0.126082i
$750$	3.71324	+	6.43152i	0.135588	+	0.234846i
$751$	25.9043	+	14.9559i	0.945263	+	0.545748i	0.891606	−	0.452812i	$-0.149579\pi$
$751$	25.9043	+	14.9559i	0.945263	+	0.545748i	0.0536565	+	0.998559i	$0.482912\pi$
$752$	−2.50586	−	9.35201i	−0.0913795	−	0.341033i
$753$		−	19.9423i		−	0.726737i
$754$	18.6512	−	16.3704i	0.679237	−	0.596175i
$755$		−	52.7104i		−	1.91833i
$756$	2.25383	−	1.38574i	0.0819708	−	0.0503988i
$757$	0.589796	−	1.02156i	0.0214365	−	0.0371291i	−0.855108	−	0.518450i	$-0.826509\pi$
$757$	0.589796	−	1.02156i	0.0214365	−	0.0371291i	0.876545	+	0.481321i	$0.159843\pi$
$758$	−15.9210	+	9.19200i	−0.578277	+	0.333868i
$759$	1.63789	+	1.63789i	0.0594515	+	0.0594515i
$760$	2.64060	+	0.707547i	0.0957847	+	0.0256654i
$761$	33.8587	+	9.07242i	1.22738	+	0.328875i	0.813558	−	0.581484i	$-0.197528\pi$
$761$	33.8587	+	9.07242i	1.22738	+	0.328875i	0.413820	+	0.910359i	$0.364194\pi$
$762$	9.20985	−	9.20985i	0.333638	−	0.333638i
$763$	−15.6933	−	14.8483i	−0.568135	−	0.537544i
$764$	7.68204	+	4.43523i	0.277927	+	0.160461i
$765$	−4.58744	+	1.22920i	−0.165859	+	0.0444419i
$766$	−9.68243			−0.349841
$767$	15.0842	−	13.2396i	0.544658	−	0.478053i
$768$		−	1.00000i		−	0.0360844i
$769$	−31.5481	+	8.45328i	−1.13765	+	0.304833i	−0.778007	−	0.628256i	$-0.783769\pi$
$769$	−31.5481	+	8.45328i	−1.13765	+	0.304833i	−0.359646	+	0.933089i	$0.617102\pi$
$770$	−53.1925	−	12.6871i	−1.91692	−	0.457213i
$771$	−12.6924	+	7.32794i	−0.457105	+	0.263909i
$772$	−2.59622	+	2.59622i	−0.0934402	+	0.0934402i
$773$	10.6566	−	39.7711i	0.383292	−	1.43047i	−0.457549	−	0.889184i	$-0.651273\pi$
$773$	10.6566	−	39.7711i	0.383292	−	1.43047i	0.840841	−	0.541282i	$-0.182061\pi$
$774$	−0.628692	+	2.34631i	−0.0225979	+	0.0843364i
$775$	−1.50618	+	1.50618i	−0.0541034	+	0.0541034i
$776$	11.5360	−	6.66032i	0.414119	−	0.239092i
$777$	3.71742	−	15.5857i	0.133362	−	0.559136i
$778$	−12.8508	+	3.44335i	−0.460722	+	0.123450i
$779$			2.83906i			0.101720i
$780$	−12.3162	+	2.45518i	−0.440992	+	0.0879096i
$781$	−79.1731			−2.83303
$782$	−0.514107	+	0.137754i	−0.0183844	+	0.00492609i
$783$	−5.96073	−	3.44143i	−0.213019	−	0.122987i
$784$	−3.15946	+	6.24643i	−0.112838	+	0.223087i
$785$	−35.8129	+	35.8129i	−1.27822	+	1.27822i
$786$	−21.7465	−	5.82696i	−0.775672	−	0.207841i
$787$	26.8450	+	7.19309i	0.956920	+	0.256406i	0.703296	−	0.710897i	$-0.251711\pi$
$787$	26.8450	+	7.19309i	0.956920	+	0.256406i	0.253624	+	0.967303i	$0.418377\pi$
$788$	−10.6555	−	10.6555i	−0.379586	−	0.379586i
$789$	10.8813	−	6.28232i	0.387384	−	0.223656i
$790$	16.1219	−	27.9239i	0.573590	−	0.993488i
$791$	−14.3142	+	8.80094i	−0.508955	+	0.312925i
$792$			5.93400i			0.210855i
$793$	−2.26881	+	34.8375i	−0.0805679	+	1.23712i
$794$		−	20.9294i		−	0.742756i
$795$	−8.77778	−	32.7591i	−0.311316	−	1.16185i
$796$	−7.45745	−	4.30556i	−0.264322	−	0.152607i
$797$	2.40148	+	4.15948i	0.0850646	+	0.147336i	0.905419	−	0.424520i	$-0.139557\pi$
$797$	2.40148	+	4.15948i	0.0850646	+	0.147336i	−0.820354	+	0.571856i	$0.806224\pi$
$798$	−0.988136	+	1.82636i	−0.0349796	+	0.0646525i
$799$	−12.7516	−	3.41677i	−0.451118	−	0.120877i
$800$	−1.84593	+	6.88911i	−0.0652635	+	0.243567i
$801$	3.93799	−	3.93799i	0.139142	−	0.139142i
$802$	−6.14113	−	10.6367i	−0.216851	−	0.375597i
$803$	21.3900	−	37.0486i	0.754837	−	1.30742i
$804$	−1.38874	−	5.18284i	−0.0489770	−	0.182785i
$805$	−3.44758	+	1.02677i	−0.121511	+	0.0361890i
$806$	−0.476667	−	0.965572i	−0.0167899	−	0.0340108i
$807$	21.5692			0.759273
$808$	17.1263	−	4.58898i	0.602501	−	0.161440i
$809$	25.3509	−	43.9090i	0.891290	−	1.54376i	0.0529601	−	0.998597i	$-0.483134\pi$
$809$	25.3509	−	43.9090i	0.891290	−	1.54376i	0.838330	−	0.545163i	$-0.183532\pi$
$810$	1.74156	+	3.01647i	0.0611922	+	0.105988i
$811$	10.8776	+	10.8776i	0.381963	+	0.381963i	0.871809	−	0.489846i	$-0.162947\pi$
$811$	10.8776	+	10.8776i	0.381963	+	0.381963i	−0.489846	+	0.871809i	$0.662947\pi$
$812$	18.2034	−	0.503633i	0.638813	−	0.0176741i
$813$	−1.23435	+	4.60664i	−0.0432904	+	0.161562i
$814$	25.4112	+	25.4112i	0.890663	+	0.890663i
$815$	−55.4724	+	32.0270i	−1.94311	+	1.12186i
$816$	−1.18083	−	0.681755i	−0.0413375	−	0.0238662i
$817$	−0.493433	−	1.84152i	−0.0172630	−	0.0644266i
$818$	−4.13880			−0.144710
$819$	0.356440	−	9.53273i	0.0124550	−	0.333101i
$820$	−12.5995			−0.439993
$821$	−2.20982	−	8.24715i	−0.0771231	−	0.287828i	0.916583	−	0.399844i	$-0.130936\pi$
$821$	−2.20982	−	8.24715i	−0.0771231	−	0.287828i	−0.993706	+	0.112017i	$0.964269\pi$
$822$	−18.5050	−	10.6838i	−0.645435	−	0.372642i
$823$	17.0903	−	9.86707i	0.595729	−	0.343944i	−0.171630	−	0.985161i	$-0.554903\pi$
$823$	17.0903	−	9.86707i	0.595729	−	0.343944i	0.767360	+	0.641217i	$0.221570\pi$
$824$	−2.08479	−	2.08479i	−0.0726269	−	0.0726269i
$825$	10.9538	−	40.8800i	0.381361	−	1.42326i
$826$	14.7220	−	0.407313i	0.512243	−	0.0141722i
$827$	8.80285	+	8.80285i	0.306105	+	0.306105i	0.843397	−	0.537292i	$-0.180553\pi$
$827$	8.80285	+	8.80285i	0.306105	+	0.306105i	−0.537292	+	0.843397i	$0.680553\pi$
$828$	0.195174	+	0.338051i	0.00678275	+	0.0117481i
$829$	11.2622	−	19.5067i	0.391152	−	0.677495i	−0.601450	−	0.798910i	$-0.705410\pi$
$829$	11.2622	−	19.5067i	0.391152	−	0.677495i	0.992602	+	0.121416i	$0.0387434\pi$
$830$	−44.4314	+	11.9054i	−1.54224	+	0.413241i
$831$	−27.1370			−0.941371
$832$	−2.99874	−	2.00189i	−0.103963	−	0.0694030i
$833$	5.22202	+	7.98933i	0.180932	+	0.276814i
$834$	−3.95633	−	14.7652i	−0.136996	−	0.511278i
$835$	−40.2138	+	69.6524i	−1.39166	+	2.41042i
$836$	−2.32867	−	4.03337i	−0.0805387	−	0.139497i
$837$	−0.211182	+	0.211182i	−0.00729951	+	0.00729951i
$838$	−8.03695	+	29.9943i	−0.277632	+	1.03614i
$839$	18.1332	+	4.85878i	0.626029	+	0.167744i	0.557867	−	0.829930i	$-0.311620\pi$
$839$	18.1332	+	4.85878i	0.626029	+	0.167744i	0.0681618	+	0.997674i	$0.478287\pi$
$840$	−8.10521	−	4.38525i	−0.279656	−	0.151306i
$841$	−9.18687	−	15.9121i	−0.316789	−	0.548694i
$842$	29.1371	+	16.8223i	1.00413	+	0.579736i
$843$	−4.44043	−	16.5719i	−0.152937	−	0.570768i
$844$		−	4.92739i		−	0.169608i
$845$	−17.2933	+	41.8482i	−0.594908	+	1.43962i
$846$			9.68192i			0.332871i
$847$	33.5519	+	54.5703i	1.15286	+	1.87506i
$848$	4.86844	−	8.43239i	0.167183	−	0.289569i
$849$	6.09314	−	3.51788i	0.209116	−	0.120733i
$850$	6.87642	+	6.87642i	0.235859	+	0.235859i
$851$	2.28343	+	0.611844i	0.0782751	+	0.0209737i
$852$	−12.8877	−	3.45324i	−0.441524	−	0.118306i
$853$	−0.958043	+	0.958043i	−0.0328028	+	0.0328028i	−0.723318	−	0.690515i	$-0.757384\pi$
$853$	−0.958043	+	0.958043i	−0.0328028	+	0.0328028i	0.690515	+	0.723318i	$0.257384\pi$
$854$	−17.6067	+	18.6086i	−0.602487	+	0.636774i
$855$	−2.36750	−	1.36688i	−0.0809668	−	0.0467462i
$856$	2.64735	−	0.709356i	0.0904846	−	0.0242453i
$857$	23.9274			0.817346			0.408673	−	0.912681i	$-0.365992\pi$
$857$	23.9274			0.817346			0.408673	+	0.912681i	$0.365992\pi$
$858$	17.7945	+	11.8792i	0.607495	+	0.405549i
$859$			9.89523i			0.337621i	0.985649	+	0.168810i	$0.0539926\pi$
$859$			9.89523i			0.337621i	−0.985649	+	0.168810i	$0.946007\pi$
$860$	8.17248	−	2.18981i	0.278679	−	0.0746719i
$861$	2.22040	−	9.30933i	0.0756712	−	0.317261i
$862$	−7.98436	+	4.60977i	−0.271948	+	0.157010i
$863$	−24.3259	+	24.3259i	−0.828065	+	0.828065i	−0.987249	−	0.159184i	$-0.949114\pi$
$863$	−24.3259	+	24.3259i	−0.828065	+	0.828065i	0.159184	+	0.987249i	$0.449114\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	−6.53614	+	24.3932i	−0.222236	+	0.829395i
$866$	−12.8219	+	12.8219i	−0.435707	+	0.435707i
$867$	13.1124	−	7.57042i	0.445319	−	0.257105i
$868$	0.183324	−	0.768609i	0.00622242	−	0.0260883i
$869$	−53.0601	+	14.2174i	−1.79994	+	0.482292i
$870$			23.9738i			0.812789i
$871$	−18.3221	−	6.21101i	−0.620820	−	0.210452i
$872$	8.16570			0.276526
$873$	−12.8667	+	3.44763i	−0.435473	+	0.116685i
$874$	−0.265321	−	0.153183i	−0.00897463	−	0.00518151i
$875$	14.2726	+	13.5041i	0.482502	+	0.456522i
$876$	5.09775	−	5.09775i	0.172237	−	0.172237i
$877$	5.13739	+	1.37656i	0.173477	+	0.0464831i	0.344512	−	0.938782i	$-0.388044\pi$
$877$	5.13739	+	1.37656i	0.173477	+	0.0464831i	−0.171035	+	0.985265i	$0.554711\pi$
$878$	−32.9141	−	8.81931i	−1.11080	−	0.297637i
$879$	13.1179	+	13.1179i	0.442455	+	0.442455i
$880$	17.8997	−	10.3344i	0.603400	−	0.348373i
$881$	26.3870	−	45.7036i	0.889001	−	1.53979i	0.0479427	−	0.998850i	$-0.484734\pi$
$881$	26.3870	−	45.7036i	0.889001	−	1.53979i	0.841058	−	0.540945i	$-0.181933\pi$
$882$	4.66850	−	5.21586i	0.157196	−	0.175627i
$883$			5.02529i			0.169115i	0.996419	+	0.0845573i	$0.0269476\pi$
$883$			5.02529i			0.169115i	−0.996419	+	0.0845573i	$0.973052\pi$
$884$	−4.40830	+	2.17622i	−0.148267	+	0.0731941i
$885$			19.3888i			0.651748i
$886$	−9.61649	−	35.8892i	−0.323072	−	1.20572i
$887$	0.688294	+	0.397387i	0.0231107	+	0.0133429i	0.511511	−	0.859277i	$-0.329086\pi$
$887$	0.688294	+	0.397387i	0.0231107	+	0.0133429i	−0.488400	+	0.872620i	$0.662419\pi$
$888$	3.02805	+	5.24474i	0.101615	+	0.176002i
$889$	16.3981	−	30.3084i	0.549975	−	1.01651i
$890$	−18.7371	−	5.02059i	−0.628069	−	0.168291i
$891$	1.53583	−	5.73180i	0.0514523	−	0.192023i
$892$	8.28247	−	8.28247i	0.277318	−	0.277318i
$893$	−3.79946	−	6.58086i	−0.127144	−	0.220220i
$894$	−0.625181	+	1.08284i	−0.0209092	+	0.0362158i
$895$	13.5555	+	50.5898i	0.453110	+	1.69103i
$896$	−0.755188	−	2.53568i	−0.0252291	−	0.0847112i
$897$	1.40444	+	0.0914651i	0.0468929	+	0.00305393i
$898$	12.0900			0.403449
$899$	−1.98556	+	0.532030i	−0.0662223	+	0.0177442i
$900$	3.56607	−	6.17661i	0.118869	−	0.205887i
$901$	−6.63817	−	11.4976i	−0.221149	−	0.383042i
$902$	15.1781	+	15.1781i	0.505374	+	0.505374i
$903$	0.177741	+	6.42428i	0.00591485	+	0.213787i
$904$	1.64378	−	6.13467i	0.0546713	−	0.204036i
$905$	−19.6269	−	19.6269i	−0.652419	−	0.652419i
$906$	−13.1056	+	7.56655i	−0.435406	+	0.251382i
$907$	7.86742	+	4.54226i	0.261233	+	0.150823i	0.624897	−	0.780707i	$-0.285141\pi$
$907$	7.86742	+	4.54226i	0.261233	+	0.150823i	−0.363664	+	0.931530i	$0.618474\pi$
$908$	−1.79513	−	6.69952i	−0.0595735	−	0.222331i
$909$	−17.7305			−0.588082
$910$	−29.3760	+	15.5266i	−0.973804	+	0.514703i
$911$	21.6692			0.717933			0.358967	−	0.933350i	$-0.383129\pi$
$911$	21.6692			0.717933			0.358967	+	0.933350i	$0.383129\pi$
$912$	−0.203136	−	0.758114i	−0.00672650	−	0.0251037i
$913$	67.8665	+	39.1828i	2.24605	+	1.29676i
$914$	5.73005	−	3.30824i	0.189533	−	0.109427i
$915$	−23.8478	−	23.8478i	−0.788383	−	0.788383i
$916$	0.304811	−	1.13757i	0.0100712	−	0.0375863i
$917$	−59.5427	+	1.64737i	−1.96627	+	0.0544010i
$918$	0.964147	+	0.964147i	0.0318216	+	0.0318216i
$919$	−14.5126	−	25.1366i	−0.478727	−	0.829180i	0.520975	−	0.853572i	$-0.325568\pi$
$919$	−14.5126	−	25.1366i	−0.478727	−	0.829180i	−0.999702	+	0.0243920i	$0.992235\pi$
$920$	0.679813	−	1.17747i	0.0224128	−	0.0388201i
$921$	−3.29688	+	0.883398i	−0.108636	+	0.0291089i
$922$	−23.2139			−0.764507
$923$	−36.1550	+	31.7337i	−1.19006	+	1.04453i
$924$	4.48128	+	15.0467i	0.147423	+	0.495001i
$925$	−11.1792	−	41.7212i	−0.367568	−	1.37178i
$926$	3.22270	−	5.58187i	0.105904	−	0.183432i
$927$	1.47417	+	2.55333i	0.0484180	+	0.0838624i
$928$	−4.86692	+	4.86692i	−0.159764	+	0.159764i
$929$	−2.84426	+	10.6149i	−0.0933173	+	0.348265i	−0.996759	−	0.0804463i	$-0.974365\pi$
$929$	−2.84426	+	10.6149i	−0.0933173	+	0.348265i	0.903442	+	0.428711i	$0.141032\pi$
$930$	1.00481	+	0.269238i	0.0329490	+	0.00882866i
$931$	−1.12635	+	5.37730i	−0.0369148	+	0.176234i
$932$	−3.41788	−	5.91995i	−0.111957	−	0.193914i
$933$	−3.38260	−	1.95295i	−0.110741	−	0.0639366i
$934$	2.85377	+	10.6504i	0.0933783	+	0.348492i
$935$		−	28.1822i		−	0.921655i
$936$	2.37843	+	2.70981i	0.0777415	+	0.0885728i
$937$			1.49801i			0.0489378i	0.999701	+	0.0244689i	$0.00778947\pi$
$937$			1.49801i			0.0489378i	−0.999701	+	0.0244689i	$0.992211\pi$
$938$	−7.43542	−	12.0933i	−0.242775	−	0.394860i
$939$	15.1436	−	26.2294i	0.494192	−	0.855966i
$940$	29.2052	−	16.8616i	0.952569	−	0.549966i
$941$	12.8482	+	12.8482i	0.418841	+	0.418841i	0.884804	−	0.465963i	$-0.154292\pi$
$941$	12.8482	+	12.8482i	0.418841	+	0.418841i	−0.465963	+	0.884804i	$0.654292\pi$
$942$	14.0453	+	3.76342i	0.457619	+	0.122619i
$943$	1.36389	+	0.365453i	0.0444143	+	0.0119008i
$944$	−3.93612	+	3.93612i	−0.128110	+	0.128110i
$945$	6.69405	+	6.33361i	0.217757	+	0.206032i
$946$	−12.4830	−	7.20707i	−0.405858	−	0.234322i
$947$	−18.3580	+	4.91900i	−0.596554	+	0.159846i	−0.544447	−	0.838795i	$-0.683260\pi$
$947$	−18.3580	+	4.91900i	−0.596554	+	0.159846i	−0.0521072	+	0.998641i	$0.516594\pi$
$948$	−9.25714			−0.300658
$949$	−5.08169	−	25.4920i	−0.164959	−	0.827504i
$950$			5.59771i			0.181614i
$951$	−22.4387	+	6.01243i	−0.727624	+	0.194966i
$952$	−3.50907	−	0.836963i	−0.113730	−	0.0271261i
$953$	−31.5430	+	18.2114i	−1.02178	+	0.589924i	−0.914619	−	0.404318i	$-0.867509\pi$
$953$	−31.5430	+	18.2114i	−1.02178	+	0.589924i	−0.107160	+	0.994242i	$0.534176\pi$
$954$	−6.88502	+	6.88502i	−0.222911	+	0.222911i
$955$	−7.99670	+	29.8441i	−0.258767	+	0.965732i
$956$	−2.51479	+	9.38532i	−0.0813341	+	0.303543i
$957$	28.8803	−	28.8803i	0.933566	−	0.933566i
$958$	5.31637	−	3.06941i	0.171764	−	0.0991682i
$959$	−54.9910	−	13.1161i	−1.77575	−	0.423542i
$960$	3.36444	−	0.901498i	0.108587	−	0.0290957i
$961$		−	30.9108i		−	0.997123i
$962$	21.7894	+	1.41905i	0.702520	+	0.0457520i
$963$	−2.74074			−0.0883191
$964$	3.78785	−	1.01495i	0.121998	−	0.0326894i
$965$	−11.0753	−	6.39434i	−0.356527	−	0.205841i
$966$	0.750190	+	0.709797i	0.0241370	+	0.0228373i
$967$	12.1331	−	12.1331i	0.390174	−	0.390174i	−0.484575	−	0.874750i	$-0.661026\pi$
$967$	12.1331	−	12.1331i	0.390174	−	0.390174i	0.874750	+	0.484575i	$0.161026\pi$
$968$	−23.3873	−	6.26661i	−0.751696	−	0.201416i
$969$	−1.03370	−	0.276978i	−0.0332071	−	0.00889781i
$970$	32.8079	+	32.8079i	1.05340	+	1.05340i
$971$	12.5245	−	7.23103i	0.401930	−	0.232055i	−0.285386	−	0.958413i	$-0.592122\pi$
$971$	12.5245	−	7.23103i	0.401930	−	0.232055i	0.687317	+	0.726358i	$0.258789\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−21.1825	−	34.4521i	−0.679080	−	1.10449i
$974$			10.9203i			0.349908i
$975$	−11.3832	−	23.0586i	−0.364553	−	0.738466i
$976$		−	9.68265i		−	0.309934i
$977$	10.5148	+	39.2419i	0.336400	+	1.25546i	0.902344	+	0.431017i	$0.141845\pi$
$977$	10.5148	+	39.2419i	0.336400	+	1.25546i	−0.565944	+	0.824443i	$0.691488\pi$
$978$	15.9261	+	9.19492i	0.509260	+	0.294021i
$979$	16.5237	+	28.6199i	0.528100	+	0.914696i
$980$	−23.8639	−	4.99865i	−0.762306	−	0.159676i
$981$	−7.88746	−	2.11344i	−0.251827	−	0.0674769i
$982$	2.12471	−	7.92953i	0.0678023	−	0.253041i
$983$	31.4962	−	31.4962i	1.00457	−	1.00457i	0.00458449	−	0.999989i	$-0.498541\pi$
$983$	31.4962	−	31.4962i	1.00457	−	1.00457i	0.999989	−	0.00458449i	$-0.00145929\pi$
$984$	1.80865	+	3.13267i	0.0576576	+	0.0998659i
$985$	26.2438	−	45.4557i	0.836198	−	1.44834i
$986$	2.42898	+	9.06506i	0.0773544	+	0.288690i
$987$	7.31167	+	24.5503i	0.232733	+	0.781444i
$988$	−2.68004	−	0.908508i	−0.0852635	−	0.0289035i
$989$	−0.948184			−0.0301505
$990$	−19.9646	+	5.34949i	−0.634515	+	0.170018i
$991$	26.2447	−	45.4571i	0.833690	−	1.44399i	−0.0614024	−	0.998113i	$-0.519557\pi$
$991$	26.2447	−	45.4571i	0.833690	−	1.44399i	0.895093	−	0.445880i	$-0.147109\pi$
$992$	0.149328	+	0.258644i	0.00474117	+	0.00821195i
$993$	−21.1578	−	21.1578i	−0.671423	−	0.671423i
$994$	−35.2869	+	0.976283i	−1.11923	+	0.0309658i
$995$	7.76291	−	28.9716i	0.246101	−	0.918461i
$996$	9.33819	+	9.33819i	0.295892	+	0.295892i
$997$	−32.9828	+	19.0426i	−1.04458	+	0.603086i	−0.921126	−	0.389265i	$-0.872729\pi$
$997$	−32.9828	+	19.0426i	−1.04458	+	0.603086i	−0.123449	+	0.992351i	$0.539396\pi$
$998$	29.6483	+	17.1175i	0.938500	+	0.541843i
$999$	−1.56744	−	5.84975i	−0.0495915	−	0.185078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.97.6	yes	40
7.6	odd	2		546.2.bx.a.97.10	✓	40
13.11	odd	12		546.2.bx.a.349.10	yes	40
91.76	even	12	inner	546.2.bx.b.349.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.10	✓	40	7.6	odd	2
546.2.bx.a.349.10	yes	40	13.11	odd	12
546.2.bx.b.97.6	yes	40	1.1	even	1	trivial
546.2.bx.b.349.6	yes	40	91.76	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.46294 - 2.46294i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.0731721 + 2.64474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.46294 - 2.46294i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.0731721 + 2.64474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.74156 - 3.01647i) q^{10} +(-5.73180 + 1.53583i) q^{11} -1.00000 q^{12} +(-2.00189 + 2.99874i) q^{13} +(-2.53568 + 0.755188i) q^{14} +(-0.901498 - 3.36444i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.681755 - 1.18083i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(0.203136 - 0.758114i) q^{19} +(3.36444 + 0.901498i) q^{20} +(-1.25900 + 2.32700i) q^{21} +(-2.96700 - 5.13899i) q^{22} +(-0.338051 - 0.195174i) q^{23} +(-0.258819 - 0.965926i) q^{24} +7.13213i q^{25} +(-3.41469 - 1.15755i) q^{26} +1.00000i q^{27} +(-1.38574 - 2.25383i) q^{28} +(-3.44143 + 5.96073i) q^{29} +(3.01647 - 1.74156i) q^{30} +(0.211182 + 0.211182i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-5.73180 - 1.53583i) q^{33} +(0.964147 - 0.964147i) q^{34} +(6.33361 - 6.69405i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-5.84975 + 1.56744i) q^{37} +0.784857 q^{38} +(-3.23306 + 1.59604i) q^{39} +3.48312i q^{40} +(-3.49404 + 0.936225i) q^{41} +(-2.57356 - 0.613830i) q^{42} +(2.10364 - 1.21454i) q^{43} +(4.19597 - 4.19597i) q^{44} +(0.901498 - 3.36444i) q^{45} +(0.101029 - 0.377047i) q^{46} +(6.84615 - 6.84615i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.98929 + 0.387042i) q^{49} +(-6.88911 + 1.84593i) q^{50} -1.36351i q^{51} +(0.234317 - 3.59793i) q^{52} +9.73688 q^{53} +(-0.965926 + 0.258819i) q^{54} +(17.8997 + 10.3344i) q^{55} +(1.81837 - 1.92185i) q^{56} +(0.554978 - 0.554978i) q^{57} +(-6.64833 - 1.78141i) q^{58} +(-5.37683 - 1.44072i) q^{59} +(2.46294 + 2.46294i) q^{60} +(8.38542 - 4.84132i) q^{61} +(-0.149328 + 0.258644i) q^{62} +(-2.25383 + 1.38574i) q^{63} +1.00000i q^{64} +(12.3162 - 2.45518i) q^{65} -5.93400i q^{66} +(1.38874 + 5.18284i) q^{67} +(1.18083 + 0.681755i) q^{68} +(-0.195174 - 0.338051i) q^{69} +(8.10521 + 4.38525i) q^{70} +(12.8877 + 3.45324i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-5.09775 + 5.09775i) q^{73} +(-3.02805 - 5.24474i) q^{74} +(-3.56607 + 6.17661i) q^{75} +(0.203136 + 0.758114i) q^{76} +(-4.48128 - 15.0467i) q^{77} +(-2.37843 - 2.70981i) q^{78} +9.25714 q^{79} +(-3.36444 + 0.901498i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.80865 - 3.13267i) q^{82} +(-9.33819 - 9.33819i) q^{83} +(-0.0731721 - 2.64474i) q^{84} +(-1.22920 + 4.58744i) q^{85} +(1.71762 + 1.71762i) q^{86} +(-5.96073 + 3.44143i) q^{87} +(5.13899 + 2.96700i) q^{88} +(-1.44141 - 5.37940i) q^{89} +3.48312 q^{90} +(-8.07737 - 5.07505i) q^{91} +0.390347 q^{92} +(0.0772979 + 0.288480i) q^{93} +(8.38479 + 4.84096i) q^{94} +(-2.36750 + 1.36688i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-3.44763 + 12.8667i) q^{97} +(-2.18282 - 6.65096i) q^{98} +(-4.19597 - 4.19597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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